Question

if x-1/x=27 then find x*4+1/x*4

Answer 1

x - 1/x = 27
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(x - 1/x)² = x² +1/x² + 2(x)(1/x)

(x and 1/x are cancelled)

=> (x - 1/x)² = x² + 1/x² + 2

=> x²+1/x² = (x-1/x)² - 2 = 27² - 2 = 729 - 2 = 727
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(x² +1/x²)² = x⁴ + 1/x⁴ + 2(x² + 1/x²)

( x² and 1/x² is deducted)

=>(x² + 1/x² ) ² = x⁴ + 1/ x⁴ + 2

=>x⁴ + 1/x⁴ = ( x² + 1/x²) ² -2 = 727² - 2 = 528529-2 = 528527

So the answer is 528527

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