Question

Calculati:
(x/x+1)^2+(x/x-1)^2=6

Answer 1

Explicație pas cu pas:

$( \frac{x }{x + 1} ) {}^{2} + ( \frac{x}{x + 1} ) {}^{2} = 6$

$\frac{ {x}^{2} }{ {(x + 1)}^{2} } + \frac{ {x}^{2} }{ {(x + 1)}^{2} } = 6$

$\frac{ {2x}^{2} }{ {(x + 1)}^{2} } = 6$

$\frac{ {2x}^{2} }{ {x}^{2} + {1}^{2} } = 6$

$\frac{ {2x}^{2} }{ {x}^{2} + 1 } = 6$

Inmultesti toata relatia cu x la a doua+1

${2x}^{2} = 6( {x}^{2} + 1)$

${2x}^{2} = {6x}^{2} + 6$

${2x}^{2} - {6x}^{2} = 6$

${4x}^{2} = 6$

${x}^{2} = 6 \div 4$

${x}^{2} = 1.5$

$x = \sqrt{1.5}$

$x = \frac{ \sqrt{150} }{ \sqrt{100} }$

$x = \frac{5 \sqrt{6} }{10}$

$x = \frac{ \sqrt{6} }{2}$

Cred ca mi-am dat gtesit da asta este...