Question

prove that x+1/x=x²+1/x²=x⁴+1/x⁴ when x-1/x=2​

Answer 1

Step-by-step explanation:

x-1/x=2

on squareing both side,

(x-1/x)²=2²

x²+1/x²+2=4

x²+1/x²=2

x²+1/x²=2

(x)²+(1/x)²+2•x•1/x=2+2•x•1/x

(x+1/x)²=2+2

(x+1/x)²=4

x+1/x=2

x²+1/x²=2

on squareing both side

(x²+1/x²)=2²

x⁴+1/x⁴+2=4

x⁴+1/x⁴=2

hence x+1/x=x²+1/x²=x⁴+1/x⁴=2

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