If x²+y²+z²=xy+yz+zx and x = 1, then find the value of (10x⁴+5y⁴+7z⁴)/(13x²y²+6y²z²+3z²x²)

If x²+y²+z²=xy+yz+zx and x = 1, then find the value of…

If $x^2+y^2+z^2=xy+yz+zx$ and x = 1, then find the value of $\frac{10x^4+5y^4+7z^4}{13x^2y^2+6y^2z^2+3z^2x^2}$

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 1.

We have been given

$x^2+y^2+z^2=xy+yz+zx$ .........(1)

x = 1

Put y = 1 and z = 1 in equation 1.

⇒ 1² + 1² + 1² = 1 + 1 + 1

⇒ 3 = 3

The equation is satisfied;

So, the value of $\frac{10x^4+5y^4+7z^4}{13x^2y^2+6y^2z^2+3z^2x^2}$

⇒ (10 + 5 + 7)/(13 + 6 + 3) = 22/22 = 1