In the following question, select the answer figure in which the question figure is hidden/embedded.

If $x^{2}+y^{2}+z^{2}=x y+y z+z x,(x eq 0)$, then the value of $frac{4 x+2 y-3 z}{2 x}$ is

x² + y² + z² = xy + yz + zx

⇒ 2x² + 2y² + 2z² – 2xy – 2yz – 2zx = 0

⇒ (x–y)² + (y–z)² + (z–x)² = 0 2 0

⇒ x – y = 0 ⇒ x = y

y – z = 0 Ÿ y = z

z – x = 0 Ÿ z = x

$herefore quad frac{4 x+2 y-3 z}{2 x}=frac{4+2-3}{2}=frac{3}{2}$

Alternative :

x² + y² + z² = xy + yz + zx

x = y = z = 1 (Let)

Clearly the value of expression on both sides be

equal.

$herefore frac{4 x+2 y-3 z}{2 x}=frac{4+2-3}{2}=frac{3}{2}$