Question

If $\displaystyle{\:x\:-\:\dfrac{1}{x}\:=\:5}$, find the value of

$\displaystyle{\:1\:.\:x^2\:+\:\dfrac{1}{x^2}}$

$\displaystyle{\:2\:.\:x^4\:+\:\dfrac{1}{x^4}}$
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Answer 1

Answer:

x²+1/x²=27

x^4 +1/x^4=727

Step-by-step explanation:

x-1/x=5

squaring we get

x²+1/x²-2x*1/x=25

x²+1/x²=25+2=27

squaring again

x^4 +1/x^4+2*x²*1/x²=27²

x^4 +1/x^4=729-2

x^4 +1/x^4=727

Answer 2

Answer:

x²+1/x² = 27

x⁴+1/x⁴ = 727

Step-by-step explanation:

x - 1/x = 5

=> (x-1/x)² = 25

=> x²+1/x²-2.x.1/x = 25

=> x²+1/x²-2 = 25

=> x²+1/x² = 27

=> (x²+1/x²)² = 729

=> x⁴+1/x⁴+2.x².1/x² = 729

=> x⁴+1/x⁴+2 = 729

=> x⁴+1/x⁴ = 727

using formula : (x-y)² = x²+y²-2.x.y

(x+y)² = x²+y²+2.x.y