SSC MTS Model Paper 2

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Question : 44 of 150

Marks: +1, -0

If x + y + z = 10,

x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 30

then the value of

x ^ { 3 } + y ^ { 3 } + z ^ { 3 } - 3 x y z

will be

–40
40
50
–50

Solution:

(4) since

x ^ { 3 } + y ^ { 3 } + z ^ { 3 } - 3 x y z

= ( x + y + z ) ( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } - x y - y z - z x )

...(i)
&

( x + y + z ) ^ { 2 } = x ^ { 2 } + y ^ { 2 } + z ^ { 2 } + 2 ( x y + y z

+ z x )

⇒

( 10 ) ^ { 2 } = 30 + 2 ( x y + y z + z x )

⇒

2 ( x y + y z + z x ) = 100 - 30 = 70

From (i),

x ^ { 3 } + y ^ { 3 } + z ^ { 3 } - 3 x y z = 10 ( 30 - 35 ) = - 50

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