Question

please help me tell fast

Answer 1

if x^2 + 1/ x^2 = 14 , then x^3 + 1/ x^3 = ?

solution :
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x^2 + 1/ x^2 = 14

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(x)^2 + ( 1/ x)^2 + 2(x)(1/x) - 2(x)(1/x) = 14

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( x + 1/x )^2 - 2 = 14

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(x + 1 /x )^2 = 16

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x + 1/ x = 4

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take cube both side , we get

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

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x^3+ 1/x^3 +3(x^2)(1/x) + 3(x) (1/x^2) = 64

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x^3 + 1/ x^3 + 3(x)+ 3 ( 1/ x) = 64

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x^3 + 1 / x^3 + 3 ( x + 1 /x ) = 64

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x^3 + 1 / x^3 + 3 ( 4 ) = 64

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x^3 + 1/ x^3 + 12 = 64

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x^3 + 1/ x^3 = 64 - 12

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x^3 + 1 /x^3 = 52

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Answer : x^3 + 1/ x^3 = 52