CMR $\frac{a^{3}}{x}+\frac{b^{3}}{y}+\frac{c^{3}}{z}\geq \frac{(a+b+c)^{3}}{3(x+y+z)}$
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Started By kangharam, 04-06-2018 - 10:46
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Posted 05-06-2018 - 08:27
$$VT= \frac{\left ( a^{\,\frac{3}{2}} \right )^{2}}{x}+ \frac{\left ( b^{\,\frac{3}{2}} \right )^{2}}{y}+ \frac{\left ( c^{\,\frac{3}{2}} \right )^{2}}{z}\geqq \frac{\left ( a^{\,\frac{3}{2}}+ b^{\,\frac{3}{2}}+ c^{\,\frac{3}{2}} \right )^{2}}{x+ y+ z}\geqq \frac{\left ( 3 \times \left ( \frac{a+ b+ c}{3} \right )^{\frac{3}{2}} \right )^{2}}{x+ y+ z}= VP$$
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