Question

знайти значення виразу​

Answer 1

${x}^{2} + \frac{1}{ {x}^{2} } = 18$

Пусть x-1/x = y:

$x - \frac{1}{x} = y \\{ (x - \frac{1}{x})^{2} } = {y}^{2} \\ {x}^{2} - 2 \times x \times \frac{1}{x} + \frac{1}{ {x}^{2} } = {y}^{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 = {y}^{2} \\ 18 - 2 = {y}^{2} \\ 16 = {y}^{2} \\ y = 4 \\ y = - 4$

Ответ : x-1/x= ±4

Answer 2

(х-(1/х))²=х²+(1/х²)-2; х²+(1/х²)=18, поэтому (х-(1/х))²=18-2;

(х-(1/х))²=16⇒(х-(1/х)=±4