Question

If x+1/x=5+√2 find x³+1/x³​

Answer 1

Answer:

The answer is $140+74\sqrt 2$

Step-by-step explanation:

Given

        $x+\dfrac{1}{x}=5+\sqrt 2$

Now using identity

        $\boxed{a^3+b^3=(a+b)^3-3ab(a+b}$

$x^3+\dfrac{1}{x^3}=(x+\dfrac{1}{x})^3-3(x)(\dfrac{1}{x})(x+\dfrac{1}{x})$

              $=(5+\sqrt 2)^3-3(5+\sqrt 2)\\=(5+\sqrt 2)[(5+\sqrt 2)^2-3]\\=(5+\sqrt 2)(25+2+10\sqrt 2-3)\\=(5+\sqrt 2)(24+10\sqrt 2)\\=120+20+50\sqrt2+24\sqrt 2\\=140+74\sqrt 2$