Chủ đề này có 2 trả lời

[RealCielo]

8,$\begin{Bmatrix} 5(3-\sqrt{5x+y})=2x-\frac{3y}{x}\\ \sqrt{2x^3-29}+\sqrt[3]{x^2+2x-9+y}=\frac{91-y-10x}{x+2} \end{Bmatrix}$

9,$\left\{\begin{matrix} x^2+2x^2y-3xy^2+x(y+1)=2y^2(5y+1)+2y\\ (x^2+17y+12)^2=4(x+y+7)(x^2+3x+8y+5) \end{matrix}\right.$

[leminhnghiatt]

8,$\begin{Bmatrix} 5(3-\sqrt{5x+y})=2x-\frac{3y}{x}\\ \sqrt{2x^3-29}+\sqrt[3]{x^2+2x-9+y}=\frac{91-y-10x}{x+2} \end{Bmatrix}$

 

ĐK: $x \not =0$

(1) $\iff 15-2x+\dfrac{3y}{x}=5\sqrt{5x+y}$ 

 

$\iff 4x^4-185x^3-37x^2+9y^2+90xy+225x^2=0$ (bình phương 2 vế rồi chuyển vế)

 

$\iff (4x^2-5x-y)(x^2-45x-9y)=0$

 

Với $4x^2-5x-y=0 \iff y=4x^2-5x$ Thay vào pt (2):

 

$\iff \sqrt{2x^3-29}+\sqrt[3]{5x^2-3x-9}+\dfrac{4x^2+5x-91}{x+2}=0$

 

$\iff (\sqrt{2x^3-29}-5)+(\sqrt[3]{5x^2-3x-9}-3)+(\dfrac{4x^2+5x-91}{x+2}+8)=0$

 

$\iff \dfrac{2(x-3)(x^2+3x+9)}{\sqrt[3]{2x^3-29}+5}+\dfrac{(x-3)(5x+12)}{\sqrt[3]{5x^2-3x-9}+3}+\dfrac{(x-3)(4x+29)}{x+2}=0$

 

$\iff (x-3)[\dfrac{2(x^2+3x+9)}{\sqrt[3]{2x^3-29}+5}+\dfrac{5x+12}{\sqrt[3]{5x^2-3x-9}+3}+\dfrac{4x+29}{x+2}]=0$

 

$\iff x=3$ (vì $\dfrac{2(x^2+3x+9)}{\sqrt[3]{2x^3-29}+5}+\dfrac{5x+12}{\sqrt[3]{5x^2-3x-9}+3}+\dfrac{4x+29}{x+2} >0$

 

 

Với $x^2-45x-9y=0$ bạn làm TT...

[Fr13nd]

 

 

Với $x^2-45x-9y=0$ bạn làm TT...

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