Question

Rezolvati in multimea numerelor reale ecuatia:
√(x+1)-√(x-1)=√2

Answer 1

Am atasat rezolvarea

Answer 2

$\sqrt{x + 1} - \sqrt{x - 1} = \sqrt{2} \: | {( \: )}^{2}$

$x + 1 - 2 \sqrt{(x + 1)(x - 1)} + x - 1 = 2$

$2x - 2 \sqrt{ {x}^{2} - 1} = 2 \: | \div 2$

$x - \sqrt{ {x}^{2} - 1} = 1$

$- \sqrt{ {x}^{2} - 1 } = 1 - x \: | \times ( - 1)$

$\sqrt{ {x}^{2} - 1} = x - 1 \: |{( \: ) }^{2}$

${x}^{2} - 1 = {x}^{2} - 2x + 1$

${x}^{2} - {x}^{2} + 2x = 1 + 1$

$2x = 2$

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

$x = 1$