Question

if x^4+1/x^4=194.Find x^3+1/x^3
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Answer 1

Answer:

52

Step-by-step explanation:

We know the identity ,

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a² + b² + 2ab = ( a + b )²

a² + b² = ( a + b )² - 2ab

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x⁴ + 1 / x⁴ = 194 ---( 1 )

( x² + 1 / x² )² - 2 = 194

( x² + 1 / x² )² = 194+2

x² + 1 /x² = √196

x² + 1 /x² = 14 -----( 2 )

( x + 1 / x )² - 2 = 14

( x + 1 / x )² = 14 +2

( x + 1/x ) =√16

x + 1 / x = 4------( 3 )

Therefore,

x³ + 1 / x³ = ( x + 1 /x )(x² + 1/x² - 1 )

=4 × ( 14 - 1 )

[ From ( 2 ) and ( 3 )

= 4 × 13

= 52

Answer 2

Step-by-step explanation:

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