Question

If x^2 +1/x^2 =98 find x^3 +1/x^3

Answer 1

970 is ur answer...first find x+1/x...then cube it

Answer 2

Solution:-

given :- x^2 +1/x^2 =98 ;- x^2 +1/x^2 =98=?

${(x + \frac{1}{x} })^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \\ {(x + \frac{1}{x} })^{2} = 98 - 2 \\ {(x + \frac{1}{x} }) = \sqrt{96} \\ {(x + \frac{1}{x} })= 4 \sqrt{6} \\ \\ {(x + \frac{1}{x} })^{3} = {x}^{3} + \frac{1}{ {x}^{3} } - 3({(x + \frac{1}{x} }) \\ {x}^{3} + \frac{1}{ {x}^{3} } = { \sqrt{96} }^{3} + 3 \sqrt{96} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 96 \sqrt{96} + 3\sqrt{96} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 99 \sqrt{96} \\ \\ {x}^{3} + \frac{1}{ {x}^{3} } = 396 \sqrt{6}$