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SSC CHSL 14 Nov 2025 Shift 2 Paper

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Question : 62 of 100

Marks: +1, -0

If

x+y+z=16

xy+yz+zx=75

, what is the value of

x^{2}+y^{2}+z^{2}

?

106
121
156
108

Solution:

Concept:

Use the algebraic identity

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

to find the sum of squares.

Explanation:

Given

x+y+z = 16

and

xy+yz+zx = 75

.

First, square the sum:

(16)^2 = 256

.

Then compute twice the sum of products:

2 \times 75 = 150

.

Rearrange the identity:

x^2+y^2+z^2 = (x+y+z)^2 - 2(xy+yz+zx)

.

Subtract:

256 - 150 = 106

.

Answer:

A. 106

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