SSC MTS Model Paper 8

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Question : 100 of 100

Marks: +1, -0

If x

^{2}

+ y

^{2}

+ z

^{2}

= 2(x + z - 1) , then the value of: x

^{3}

+ y

^{3}

+ z

^{3}

= ?

2
0
-1
1

Solution:

x

^{2}

+ y

^{2}

+ z

^{2}

=2(x + z — 1)
= x

^{2}

+ y

^{2}

+ z

^{2}

= 2x + 2z — 2
= x

^{2}

- 2x + y

^{2}

+ z

^{2}

- 2z + 2 = 0
= x

^{2}

- 2x + 1+ y

^{2}

+ z

^{2}

— 2z+ 1 = 0
= (x — 1 )

^{2}

+ y

^{2}

+ (z — 1 )

^{2}

= 0
[a

^{2}

+ b

^{2}

+ c

^{2}

= 0 = a = 0, b =0, c = 0]
x —1 = 0 = x = 1
y = 0
z — 1 = 0 = z = 1
x

^{3}

+ y

^{3}

+ z

^{3}

= 1 + 0 + 1 = 2

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