Question : $If x^{2} + y^{2} + z^{2} = x y + y z + z x and x = 1, then find the value of \frac{10 x^{4} + 5 y^{4} + 7 z^{4}}{13 x^{2} y^{2} + 6 y^{2} z^{2} + 3 z^{2} x^{2}}$ .
Option 1: 2
Option 2: 0
Option 3: –1
Option 4: 1

Question

Question : If $x + y + z = 0$ , then what is the value of $\frac{x^{2}}{(y z)} + \frac{y^{2}}{(x z)} + \frac{z^{2}}{(x y)}$ ?

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Answer 1

Correct Answer: 1

Solution : $x^{2} + y^{2} + z^{2} = x y + y z + z x$
$\Rightarrow \frac{1}{2} [(x - y)^{2} + (y - z)^{2} + (z - x)^{2}] = 0$
$\Rightarrow x = y, y = z,$ and $z = x$
As $x = 1$ , so $y = z = 1$
So, $\frac{10 x^{4} + 5 y^{4} + 7 z^{4}}{13 x^{2} y^{2} + 6 y^{2} z^{2} + 3 z^{2} x^{2}}$
$= \frac{10 (1)^{4} + 5 (1)^{4} + 7 (1)^{4}}{13 (1)^{2} (1)^{2} + 6 (1)^{2} (1)^{2} + 3 (1)^{2} (1)^{2}}$
$= \frac{22}{22}$
$= 1$
Hence, the correct answer is 1.

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Question : If x2+y2+z2=xy+yz+zx and x=1, then find the value of 10x4+5y4+7z413x2y2+6y2z2+3z2x2.Option 1: 2Option 2: 0Option 3: –1Option 4: 1

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Question : $If x^{2} + y^{2} + z^{2} = x y + y z + z x and x = 1, then find the value of \frac{10 x^{4} + 5 y^{4} + 7 z^{4}}{13 x^{2} y^{2} + 6 y^{2} z^{2} + 3 z^{2} x^{2}}$ .
Option 1: 2
Option 2: 0
Option 3: –1
Option 4: 1