Chủ đề này có 10 trả lời

[donghaidhtt]

giải pt: $\frac{2}{3}\sqrt{4x+1}-9x^{2}+26x-\frac{37}{3}=0$

Bài viết đã được chỉnh sửa nội dung bởi donghaidhtt: 19-06-2012 - 01:05

[T M]

giải pt: $\frac{2}{3}\sqrt{4x+1}-9x^{2}+26x+\frac{37}{3}=0$

http://www.wolframal...+\frac{37}{3}=0

Nghiệm này thì giải làm sao được ?

[donghaidhtt]

Đây là đề thầy cho nên ko sai đâu

[nthoangcute]

giải pt: $\frac{2}{3}\sqrt{4x+1}-9x^{2}+26x+\frac{37}{3}=0$

Ta có: ĐKXĐ: $x \geq \frac{-1}{4}$
Đặt $\sqrt{4x+1}=a \geq 0$
Suy ra $x=\frac{a^2-1}{4}$
Từ giả thiết suy ra:
$$\frac{2}{3}a- 9(\frac{a^2-1}{4})^2+26.\frac{a^2-1}{4}+\frac{37}{3}=0$$
$$\Leftrightarrow 32a-27a^4+366a^2+253=0$$
$$\Leftrightarrow a^4=\frac{122}{9}a^2+\frac{32}{27}a+\frac{253}{27}$$
$$\Leftrightarrow a^4 +2.a^2.(-\frac{2}{27}\sqrt[3]{80243+12\sqrt{44388147}}- \frac{722}{27\sqrt[3]{80243+12\sqrt{44388147}}}-\frac{61}{27})+((-\frac{2}{27}\sqrt[3]{80243+12\sqrt{44388147}}- \frac{722}{27\sqrt[3]{80243+12\sqrt{44388147}}}-\frac{61}{27}))^2$$
$$=\frac{122}{9}a^2+\frac{32}{27}a+\frac{253}{27}+2.a^2.(-\frac{2}{27}\sqrt[3]{80243+12\sqrt{44388147}}- \frac{722}{27\sqrt[3]{80243+12\sqrt{44388147}}}-\frac{61}{27})+((-\frac{2}{27}\sqrt[3]{80243+12\sqrt{44388147}}- \frac{722}{27\sqrt[3]{80243+12\sqrt{44388147}}}-\frac{61}{27}))^2$$
$$\Leftrightarrow {\frac {1}{12381017456889}}\, \left( 3518667\,{a}^{2}-260642\,\sqrt [3
]{80243+12\,\sqrt {44388147}}-160486\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}+24\, \left( 80243+12\,\sqrt {44388147}
\right) ^{2/3}\sqrt {44388147}-7949581 \right) ^{2}$$
$$={\frac {4}{4840519727997694107}}\, \left( -130321\,\sqrt [3]{80243+12
\,\sqrt {44388147}}-80243\, \left( 80243+12\,\sqrt {44388147} \right)
^{2/3}+12\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}\sqrt {
44388147}+7949581 \right) \left( -418762\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}-36489880+61\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}\sqrt {44388147}+361\,\sqrt [3]{80243+12\,
\sqrt {44388147}}\sqrt {44388147}-3076442\,\sqrt [3]{80243+12\,\sqrt {
44388147}}-1172889\,a \right) ^{2}$$
$$\Leftrightarrow ({\frac {2}{3810716361}}\,\sqrt {-390963\,\sqrt [3]{80243+12\,\sqrt {
44388147}}-240729\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}+
36\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}\sqrt {44388147}+
23848743} \left( -418762\, \left( 80243+12\,\sqrt {44388147} \right) ^
{2/3}-36489880+61\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}
\sqrt {44388147}+361\,\sqrt [3]{80243+12\,\sqrt {44388147}}\sqrt {
44388147}-3076442\,\sqrt [3]{80243+12\,\sqrt {44388147}}-1172889\,a
\right) +{a}^{2}-{\frac {2}{27}}\,\sqrt [3]{80243+12\,\sqrt {44388147
}}-{\frac {160486}{3518667}}\, \left( 80243+12\,\sqrt {44388147}
\right) ^{2/3}+{\frac {8}{1172889}}\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}\sqrt {44388147}-{\frac {61}{27}})$$
$$({\frac {2}{3810716361}}\,\sqrt {-390963\,\sqrt [3]{80243+12\,\sqrt {
44388147}}-240729\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}+
36\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}\sqrt {44388147}+
23848743} \left( -418762\, \left( 80243+12\,\sqrt {44388147} \right) ^
{2/3}-36489880+61\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}
\sqrt {44388147}+361\,\sqrt [3]{80243+12\,\sqrt {44388147}}\sqrt {
44388147}-3076442\,\sqrt [3]{80243+12\,\sqrt {44388147}}-1172889\,a
\right) -{a}^{2}+{\frac {2}{27}}\,\sqrt [3]{80243+12\,\sqrt {44388147
}}+{\frac {160486}{3518667}}\, \left( 80243+12\,\sqrt {44388147}
\right) ^{2/3}-{\frac {8}{1172889}}\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}\sqrt {44388147}+{\frac {61}{27}})=0$$
Xét $$({\frac {2}{3810716361}}\,\sqrt {-390963\,\sqrt [3]{80243+12\,\sqrt {
44388147}}-240729\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}+
36\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}\sqrt {44388147}+
23848743} \left( -418762\, \left( 80243+12\,\sqrt {44388147} \right) ^
{2/3}-36489880+61\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}
\sqrt {44388147}+361\,\sqrt [3]{80243+12\,\sqrt {44388147}}\sqrt {
44388147}-3076442\,\sqrt [3]{80243+12\,\sqrt {44388147}}-1172889\,a
\right) +{a}^{2}-{\frac {2}{27}}\,\sqrt [3]{80243+12\,\sqrt {44388147
}}-{\frac {160486}{3518667}}\, \left( 80243+12\,\sqrt {44388147}
\right) ^{2/3}+{\frac {8}{1172889}}\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}\sqrt {44388147}-{\frac {61}{27}})=0$$
$$\Leftrightarrow -{a}^{2}-{\frac {2}{3249}}\,\sqrt {-390963\,\sqrt [3]{80243+12\,\sqrt {
44388147}}-240729\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}+
36\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}\sqrt {44388147}+
23848743}a+{\frac {2}{3810716361}}\,\sqrt {-390963\,\sqrt [3]{80243+12
\,\sqrt {44388147}}-240729\, \left( 80243+12\,\sqrt {44388147}
\right) ^{2/3}+36\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}
\sqrt {44388147}+23848743} \left( -418762\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}-36489880+61\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}\sqrt {44388147}+361\,\sqrt [3]{80243+12\,
\sqrt {44388147}}\sqrt {44388147}-3076442\,\sqrt [3]{80243+12\,\sqrt {
44388147}} \right) +{\frac {8}{1172889}}\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}\sqrt {44388147}-{\frac {61}{27}}-{\frac {2}{
27}}\,\sqrt [3]{80243+12\,\sqrt {44388147}}-{\frac {160486}{3518667}}
\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}=0$$
Đây là phương trình bậc 2 ẩn $a$ và có
$$\Delta ={\frac {4}{27}}\,\sqrt [3]{80243+12\,\sqrt {44388147}}+{\frac {320972}
{3518667}}\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}-{\frac {
16}{1172889}}\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}\sqrt
{44388147}+{\frac {488}{27}}+{\frac {8}{3810716361}}\,\sqrt {-390963\,
\sqrt [3]{80243+12\,\sqrt {44388147}}-240729\, \left( 80243+12\,\sqrt
{44388147} \right) ^{2/3}+36\, \left( 80243+12\,\sqrt {44388147}
\right) ^{2/3}\sqrt {44388147}+23848743} \left( -418762\, \left(
80243+12\,\sqrt {44388147} \right) ^{2/3}-36489880+61\, \left( 80243+
12\,\sqrt {44388147} \right) ^{2/3}\sqrt {44388147}+361\,\sqrt [3]{
80243+12\,\sqrt {44388147}}\sqrt {44388147}-3076442\,\sqrt [3]{80243+
12\,\sqrt {44388147}} \right) <0
$$
Suy ra phương trình bậc 2 này không có nghiệm :
____________________________

Xét phương trình:
$${a}^{2}-{\frac {2}{3249}}\,\sqrt {-390963\,\sqrt [3]{80243+12\,\sqrt {
44388147}}-240729\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}+
36\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}\sqrt {44388147}+
23848743}a+{\frac {2}{3810716361}}\,\sqrt {-390963\,\sqrt [3]{80243+12
\,\sqrt {44388147}}-240729\, \left( 80243+12\,\sqrt {44388147}
\right) ^{2/3}+36\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}
\sqrt {44388147}+23848743} \left( -418762\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}-36489880+61\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}\sqrt {44388147}+361\,\sqrt [3]{80243+12\,
\sqrt {44388147}}\sqrt {44388147}-3076442\,\sqrt [3]{80243+12\,\sqrt {
44388147}} \right) +{\frac {8}{1172889}}\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}\sqrt {44388147}-{\frac {61}{27}}-{\frac {2}{
27}}\,\sqrt [3]{80243+12\,\sqrt {44388147}}-{\frac {160486}{3518667}}
\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}=0$$
Tương tự như phương trình kia ta tìm được
$$a={\frac {1}{3249}}\,\sqrt {-390963\,\sqrt [3]{80243+12\,\sqrt {
44388147}}-240729\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}+
36\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}\sqrt {44388147}+
23848743}+{\frac {1}{61731}}\,\sqrt {141137643\,\sqrt [3]{80243+12\,
\sqrt {44388147}}+86903169\, \left( 80243+12\,\sqrt {44388147}
\right) ^{2/3}-12996\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/
3}\sqrt {44388147}+17218792446+837524\,\sqrt {-390963\,\sqrt [3]{80243
+12\,\sqrt {44388147}}-240729\, \left( 80243+12\,\sqrt {44388147}
\right) ^{2/3}+36\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}
\sqrt {44388147}+23848743} \left( 80243+12\,\sqrt {44388147} \right) ^
{2/3}+72979760\,\sqrt {-390963\,\sqrt [3]{80243+12\,\sqrt {44388147}}-
240729\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}+36\, \left(
80243+12\,\sqrt {44388147} \right) ^{2/3}\sqrt {44388147}+23848743}-
122\,\sqrt {-390963\,\sqrt [3]{80243+12\,\sqrt {44388147}}-240729\,
\left( 80243+12\,\sqrt {44388147} \right) ^{2/3}+36\, \left( 80243+12
\,\sqrt {44388147} \right) ^{2/3}\sqrt {44388147}+23848743} \left(
80243+12\,\sqrt {44388147} \right) ^{2/3}\sqrt {44388147}-722\,\sqrt {
-390963\,\sqrt [3]{80243+12\,\sqrt {44388147}}-240729\, \left( 80243+
12\,\sqrt {44388147} \right) ^{2/3}+36\, \left( 80243+12\,\sqrt {
44388147} \right) ^{2/3}\sqrt {44388147}+23848743}\sqrt [3]{80243+12\,
\sqrt {44388147}}\sqrt {44388147}+6152884\,\sqrt {-390963\,\sqrt [3]{
80243+12\,\sqrt {44388147}}-240729\, \left( 80243+12\,\sqrt {44388147}
\right) ^{2/3}+36\, \left( 80243+12\,\sqrt {44388147} \right) ^{2/3}
\sqrt {44388147}+23848743}\sqrt [3]{80243+12\,\sqrt {44388147}}}$$Suy ra $$x=\frac{a^2-1}{4}={\frac {13}{9}}+1/27\,\sqrt {3}\sqrt {{\frac {280\,\sqrt [3]{21875194+
3\,\sqrt {44388147}}+ \left( 21875194+3\,\sqrt {44388147} \right) ^{2/
3}+78217}{\sqrt [3]{21875194+3\,\sqrt {44388147}}}}}+1/27\,\sqrt {{
\frac {1680\,\sqrt [3]{21875194+3\,\sqrt {44388147}}\sqrt {{\frac {280
\,\sqrt [3]{21875194+3\,\sqrt {44388147}}+ \left( 21875194+3\,\sqrt {
44388147} \right) ^{2/3}+78217}{\sqrt [3]{21875194+3\,\sqrt {44388147}
}}}}-3\,\sqrt {{\frac {280\,\sqrt [3]{21875194+3\,\sqrt {44388147}}+
\left( 21875194+3\,\sqrt {44388147} \right) ^{2/3}+78217}{\sqrt [3]{
21875194+3\,\sqrt {44388147}}}}} \left( 21875194+3\,\sqrt {44388147}
\right) ^{2/3}-234651\,\sqrt {{\frac {280\,\sqrt [3]{21875194+3\,
\sqrt {44388147}}+ \left( 21875194+3\,\sqrt {44388147} \right) ^{2/3}+
78217}{\sqrt [3]{21875194+3\,\sqrt {44388147}}}}}+36\,\sqrt {3}\sqrt [
3]{21875194+3\,\sqrt {44388147}}}{\sqrt [3]{21875194+3\,\sqrt {
44388147}}\sqrt {{\frac {280\,\sqrt [3]{21875194+3\,\sqrt {44388147}}+
\left( 21875194+3\,\sqrt {44388147} \right) ^{2/3}+78217}{\sqrt [3]{
21875194+3\,\sqrt {44388147}}}}}}}}$$

________________________
Có bạn nào giống kết quả không !!!

Bài viết đã được chỉnh sửa nội dung bởi nthoangcute: 18-06-2012 - 23:31

[donghaidhtt]

Bạn dùng phần mềm để giải pt này à?

[nthoangcute]

Bạn dùng phần mềm để giải pt này à?

He he ! Thì là mà http://www.wolframalpha.com/

[tieulyly1995]

giải pt: $\frac{2}{3}\sqrt{4x+1}-9x^{2}+26x+\frac{37}{3}=0$

Ta có :
$PT\Leftrightarrow (\sqrt{4x+1}+\frac{1}{3})^{2}= (3x-\frac{11}{3})^{2}$

[nthoangcute]

Ta có :
$PT\Leftrightarrow (\sqrt{4x+1}+\frac{1}{3})^{2}= (3x-\frac{11}{3})^{2}$

Chị Ly ơi, nhầm dấu rồi @@@

[donghaidhtt]

Ta có :
$PT\Leftrightarrow (\sqrt{4x+1}+\frac{1}{3})^{2}= (3x-\frac{11}{3})^{2}$

hic, mình cũng nghĩ như thế này. Ai dè... cái đề sai, may nhờ bạn tieulyly1995 chỉ ra giúp, mình đã sửa cái đề, mong bạn Mod nào sửa tên chủ đề với.
Thành thật xin lỗi mọi người đã đau đầu nhức óc với cái đề này

Bài viết đã được chỉnh sửa nội dung bởi donghaidhtt: 19-06-2012 - 00:01

[nthoangcute]

hic, mình cũng nghĩ như thế này. Ai dè... cái đề sai, may nhờ bạn tieulyly1995 chỉ ra giúp, mình đã sửa cái đề, mong bạn Mod nào sửa tên chủ đề với.
Thành thật xin lỗi mọi người đã đau đầu nhức óc với cái đề này

Ọe, lại sửa đề !!!
Phí cả công trình nghiên cứu cách giải phương trình bậc 4 của em, phí quá @@@

[khanh3570883]

giải pt: $\frac{2}{3}\sqrt{4x+1}-9x^{2}+26x-\frac{37}{3}=0$

Đặt: $\sqrt {4x + 1} = 3y - 4$
Khi đó ta có hệ:
\[\left\{ \begin{array}{l}
9{x^2} = 2y + 26x - 15 \\
9{y^2} = 4x + 24y - 15 \\
\end{array} \right.\]

Việc còn lại chắc ai cũng biết.