Question

ів за правильну відповідь, завдання ДУЖЕ легкі! Дякую за до ..)

Answer 1

$1)x+\frac{1}{x}=3\\\\(x+\frac{1}{x})^{2} =3^{2}\\\\x^{2}+2*x*\frac{1}{x}+\frac{1}{x^{2} }=9\\\\x^{2} +2+\frac{1}{x^{2} } =9\\\\\boxed{x^{2}+\frac{1}{x^{2} }=7}\\\\\\2)x-\frac{1}{x} =-6\\\\(x-\frac{1}{x})^{3} =(-6 )^{3}\\\\x^{3}-3*x^{2} *\frac{1}{x}+3*x*\frac{1}{x^{2} }-\frac{1}{x^{3} } =-216\\\\x^{3}-3x+\frac{3}{x}-\frac{1}{x^{3}} =-216 \\\\x^{3}-3\underbrace{(x-\frac{1}{x})}_{-6}-\frac{1}{x^{3}} =-216\\\\x^{3}-3*(-6)-\frac{1}{x^{3} }=-216$

$x^{3}+18-\frac{1}{x^{3} }=-216\\\\x^{3}-\frac{1}{x^{3} }=-216-18\\\\\boxed{x^{3}-\frac{1}{x^{3} }=-234}$