Question

if the value of x-1/x=√5 then,find the value of x³+1/x³

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Answer 1

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if the value of x-1/x=√5 then,find the value of x³+1/x³

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$\red{GIVEN}:- \\ \sf{x+\frac{1}{x}} \\ \red{TO FIND}:- \\ \sf{x^3+\frac{1}{x^3}} \\ Now, \\ (x+\frac{1}{x})^3 \\ =x^3+\frac{1}{x^3}×3×x×\frac{1}{x}(x+\frac{1}{x}) \\ Now put the values, \\ (5)^3=x^3+\frac{1}{x^3}×3(5) \\ 125-15=x^3+\frac{1}{x^3}\\ 110=x^3+\frac{1}{x^3}$

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