Question 112

If $$x+\frac{1}{x}=2$$ then the value of $$(x^2+\frac{1}{x^2})(x^3+\frac{1}{x^3})$$ is

Solution

$$(x^2+\frac{1}{x^2})$$ = $$(x + \frac{1}{x})^2$$ - 2

and

$$(x^3 + (\frac{1}{x})^3)$$ = $$(x + \frac{1}{x})$$ ($$(x + 1/$$(x)$$)^2$$ -3)

so the value of

$$(x^2+\frac{1}{x^2})(x^3+\frac{1}{x^3})$$ = (4-2)(2 (4-3)) = 4

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