Question

х^2+1/x^2=14

Найти x+1/x

Answer 1

Объяснение:

$x^2+\frac{1}{x^2} =14\ \ \ \ \ \ \ x+\frac{1}{x} =?\\(x+\frac{1}{x})^2=x^2+2*x*\frac{1}{x} +(\frac{1}{x})^2}=x^2+2+\frac{1}{x^2} \ \ \ \ \Rightarrow\\x^2+2+\frac{1}{x^2} =14+2\\(x+\frac{1}{x})^2 =16\\(x+\frac{1}{x})^2-4^2=0\\(x+\frac{1}{x}+4)(x+\frac{1}{x}-4)=0\\x+\frac{1}{x}+4=0\\x+\frac{1}{x}=-4.\\x+\frac{1}{x}-4=0\\x+\frac{1}{x}=4.$

Ответ: x+1/x=±4.