If x²+ y²+ z² = xy+yz+zx, then the value of ((17x⁴+9y⁴+16x⁴)/(8x²y²+6y²z²+10z²x²) ) is:

If x²+ y²+ z² = xy+yz+zx, then the value of…

If $x^2+ y^2+ z^2 = xy+yz+zx,$ then the value of $\left (\frac{17x^4+9y^4+16x^4}{8x^2y^2+6y^2z^2+10z^2x^2}\right )$ is:

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Correct answer: D

Explanation

The correct answer is Option 4 i.e. 1.75.

$x^2+ y^2+ z^2 = xy+yz+zx$

x² + y² + z² - xy - yz - zx = 0

⇒ $1\over2$ [(x - y)² + (y - z)² + (z - x)²] = 0

⇒ x = y = z

$\left (\frac{17x^4+9y^4+16x^4}{8x^2y^2+6y^2z^2+10z^2x^2}\right )$ = $\frac{(17+9+16)x^4}{(8+6+10)x^4}$ = $42\over24$ = $7\over4$ = 1.75