Question

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

Answer 1

hi friend!

Here is your Answer
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apply the formula
$(a + b {)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ (x + \frac{1}{x} {)}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ putting \: value \\ \\ (x + \frac{1}{x} {)}^{2} =9 8 + 2 \\ (x + \frac{1}{x} {)}^{2} = 100 \\ (x + \frac{1}{x} ) = \sqrt{100} = 10 \\ \\ (x + \frac{1}{x} {)}^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3(x + \frac{1}{x} \\ {10}^{3} = {x}^{3} + \frac{1}{ {x}^{3} } + 3 \times 10 \\ {x}^{3} + \frac{1}{ {x}^{3} } = 1000 - 30 \\ {x}^{3} + \frac{1}{ {x}^{3} } = 970 \: ans \\ \\ hope \: its \: helpful$