Question

If x ^2+1/x^2=7 find the value of 2x^2-2/x^2.

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } + 2 \times x \times \frac{1}{x} = 7 + 2 \: \: \\ (x + \frac{1}{x}) {}^{2} = 9........ (1) \\ (x + \frac{1}{x} ) = 3 \: \: \\ using \: equation \: (1) \\ (x + \frac{1}{x} ) ^{2} - 4 = 5 \\ (x - \frac{1}{x} ) = \sqrt{5} \: \: \: \: \: ...........(2) \\ multiplying \: eqution \: (1)and \: (2) \\ {x}^{2} - \frac{1}{ {x}^{2} } = 9 \sqrt{5}$