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If x2+1/x2 =7,x>0;find the value of x3+1/x3 and x-1/x

x^{2} + \frac{1}{x^{2}} = 7 {(x + \frac{1}{x})}^{2} - 2 . x . \frac{1}{x} = 7 {(x + \frac{1}{x})}^{2} = 9 x + \frac{1}{x} = 3 a) x^{3} + \frac{1}{x^{3}} = {(x + \frac{1}{x})}^{3} - 3 x . \frac{1}{x} (x + \frac{1}{x}) = {(3)}^{3} - 3 (3) = 27 - 9 = 18 ANS . . b) x^{2} + \frac{1}{x^{2}} = 7 {(x - \frac{1}{x})}^{2} + 2 . x . \frac{1}{x} = 7 {(x - \frac{1}{x})}^{2} = 5 x - \frac{1}{x} = \sqrt{5} ANS . . .

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