Question

Паже найдите по Т.Виета обязательно

Answer 1

$\displaystyle\bf\\x^{2} +9x-22=0\\\\Teorema \ Vieta \ :\\\\x_{1} +x_{2} =-9\\\\x_{1} \cdot x_{2} =-22\\\\\\1)\\\\\frac{1}{x_{1} } +\frac{1}{x_{2} } =\frac{x_{1} + x_{2} }{x_{1} \cdot x_{2} } =\frac{-9}{-22} =\frac{9}{22} \\\\\\\boxed{\frac{1}{x_{1} } +\frac{1}{x_{2} } =\frac{9}{22} }\\\\2)\\\\x_{1} ^{2} +x_{2} ^{2} =(x_{1} + x_{2} )^{2} -2\cdot x_{1} \cdot x_{2} =(-9)^{2} -2\cdot(-22)=\\\\\\=81+44=125\\\\\\\boxed{x_{1} ^{2} +x_{2} ^{2} =125}$