Question

If x²+1/x²=7 find the value of x³+1/x³ taking only the positive value of x+1/x
value of x³+1)x³taking only the positive value of x+1/x

Answer 1

Answer:

${(x + \frac{1}{x}) }^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ = 7 + 2 = 9 \\ x + \frac{1}{x} = 3 \\ {(x + \frac{1}{x}) }^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3x + \frac{3}{x} \\ = {x}^{3} + \frac{1}{ {x}^{3} } + 3(x + \frac{1}{x} ) \\ ( {3})^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times 3 \\ 27 - 9 = {x}^{3} + \frac{1}{ {x}^{3} } \\ {x}^{3} + \frac{1}{ {x}^{3} } = 18$