RRB NTPC Mains or Stage 2 Model Paper 9 with solutions

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Question : 38 of 120

Marks: +1, -0

If

x^2 + y^2 + z^2 = xy + yz + zx, (x ≠ 0)

, then the value of

{4x+ 2y -3z }/{2x}

is

0
1
$3 /2$
$1/ 2$

Solution:

(c)

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

Multiply both sieds by 2.

∴ 2(x^2 + y^2 + z^2)

= 2(xy + yz + zx)

⇒2x^2 + 2y^2 + 2z^2 – 2xy – 2yz – 2zx = 0

⇒ (x – y)^2 + (y – z)^2 + (z – x)^2 = 0

⇒ x – y = 0 ⇒ x = y

y – z = 0 ⇒ y = z

z – x = 0 ⇒ z = x

∴

{4x +2y- 3z}/{2x}={4 +2- 3} / 2=3/2

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