Question

if x^2 +1/x^2 is = 7 . find thr value of x^3+1/x^3

Answer 1

x² + 1/x² = 7


Add 2x × 1/x on both sides.


=>>
${x}^{2} + \frac{1}{ {x}^{2} } + 2x \times \frac{1}{x} = 7 + 2x \times \frac{1}{x} \\ \\ = > (x + \frac{1}{x} ) {}^{2} = 7 + 2 \\ \\ = > (x + \frac{1}{x} ) {}^{2} = 9 \\ \\ = > x + \frac{1}{x} = \sqrt{9} \\ \\ = > x + \frac{1}{x} = 3$

Now x³ + 1/x³ =
$(x + \frac{1}{x} )({x}^{2} + \frac{1}{ {x}^{2}} - x \times \frac{1}{x} )$


as, a³ + b³ = (a + b)(a² + b² - ab)

=> x³ + 1/x³ =
$(3)(7 - 1) \\ \\ = (3)(6) \\ = 18$


Hence, x³ + 1/x³ = 18

Answer 2

Hope this will help you