Question

известно что x^3+49/x^2=50. найдите значение выражения x-7/x

Answer 1

$\displaystyle\bf\\x^{2} +\frac{49}{x^{2} } =50\\\\\\x^{2} +\Big(\frac{7}{x} \Big)^{2} =50\\\\\\\Big(x-\frac{7}{x} \Big)^{2} +2\cdot x\cdot \frac{7}{x} =50\\\\\\\Big(x-\frac{7}{x} \Big)^{2} +14=50\\\\\\\Big(x-\frac{7}{x} \Big)^{2} =50-14\\\\\\\Big(x-\frac{7}{x} \Big)^{2} =36\\\\\\\left[\begin{array}{ccc}x-\dfrac{7}{x} =-6\\x-\dfrac{7}{x} =6\end{array}\right\\\\\\Otvet \ : \ -6 \ ; \ 6$