Question

If x+y+z=0 then prove that x 2 /yz + y 2 /zx + z 2 /xy=3

Answer 1

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Answer 2

Answer:

$If\: x+y+z=0 \: then \\\frac{x^{2}}{yz}+\frac{y^{2}}{zx}+\frac{z^{2}}{xy}=3$

Step-by-step explanation:

$Given \: x+y+z=0---(1)$

$LHS=\frac{x^{2}}{yz}+\frac{y^{2}}{zx}+\frac{z^{2}}{xy}\\=\frac{x^{3}+y^{3}+z^{3}}{xyz}\\=\frac{(x+y+z)(x^{2}+y^{2}+z^{2}-xy-yz-zx)+3xyz}{xyz}\\=\frac{0\times (x^{2}+y^{2}+z^{2}-xy-yz-zx)+3xyz}{xyz}$

/* From (1) */

$=\frac{3xyz}{xyz}$

$= 3\\=RHS$

Therefore.,

$If\: x+y+z=0 \: then \\\frac{x^{2}}{yz}+\frac{y^{2}}{zx}+\frac{z^{2}}{xy}=3$

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