Question

Відомо, що x+1/x=9.Знайдіть значення виразу x²+1/x²​

Answer 1

$\displaystyle\bf\\x+\frac{1}{x} =9\\\\\\\Big(x+\frac{1}{x} \Big)^{2} =9^{2} \\\\\\x^{2} +2\cdot \underbrace{x\cdot \frac{1}{x} }_{1}+\Big(\frac{1}{x} \Big)^{2} =81\\\\\\x^{2} +2+\frac{1}{x^{2} } =81\\\\\\x^{2} +\frac{1}{x^{2} } =81-2\\\\\\x^{2} +\frac{1}{x^{2} } =79\\\\\\Otvet \ : \ x^{2} +\frac{1}{x^{2} } =79$