If x ^ { 2 } + { 1 }/ { x ^ { 2 } } = 98 ( x > 0 ) , then the value of ( x ^ { 3 } + { 1 }/ { x ^ { 3 } } ) is

SSC CGL Tier II 12 Jan 2017 Paper 1

Question : 66 of 100

Marks: +1, -0

x ^ { 2 } + { 1 }/ { x ^ { 2 } } = 98 ( x > 0 ) ,

then the value of

( x ^ { 3 } + { 1 }/ { x ^ { 3 } } )

Solution:

( 1 ) x ^ { 2 } + { 1 }/ { x ^ { 2 } } = 98

⇒( x + { 1 }/ { x } ) ^ { 2 } - 2 = 98

⇒( x + { 1 }/ { x } ) ^ { 2 } = 98 + 2 = 100

⇒ x + { 1 } /{ x } = √ { 100 } = 10 ...(i)

On cubing both sides,

( x + { 1 }/ { x } ) ^ { 3 } = ( 10 ) ^ { 3 } = 1000

⇒ x ^ { 3 } + { 1 } /{ x ^ { 3 } } + 3 ( x + { 1 } /{ x } ) = 1000

⇒ x ^ { 3 } + { 1 }/ { x ^ { 3 } } + 3× 10 = 1000

⇒ x ^ { 3 } + { 1 } /{ x ^ { 3 } } = 1000 - 30 = 970

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