If $$x+\frac{1}{x}=5$$, then $$x^{6}+\frac{1}{x^{6}}$$ is
Expression : $$x+\frac{1}{x}=5$$
Cubing both sides, we get :
=> $$(x + \frac{1}{x})^3 = 5^3$$
=> $$x^3 + \frac{1}{x^3} + 3.x.\frac{1}{x}.(x + \frac{1}{x}) = 125$$
=> $$x^3 + \frac{1}{x^3} + 15 = 125$$
=> $$x^3 + \frac{1}{x^3} = 110$$
Now, squaring both sides, we get :
=> $$x^6 + \frac{1}{x^6} + 2 = 12100$$
=> $$x^6 + \frac{1}{x^6} = 12098$$
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