Question

$\sqrt{x - 1} + 1 = \sqrt{x + \sqrt{x + 8} }$
Sa se rezolve ecuatia​

Answer 1

Răspuns:

$x=4$

Explicație pas cu pas:

$\sqrt{x-1} +1=\sqrt{x+\sqrt{x+8} } \\(\sqrt{x-1} +1)^2=(\sqrt{x+\sqrt{x+8} } )^2\\x+2\sqrt{x-1} =x+\sqrt{x+8} |-x\\2\sqrt{x-1} =\sqrt{x+8} \\(2\sqrt{x-1} )^2=(\sqrt{x+8} )^2\\4(x-1)=x+8\\4x-4=x+8|+4\\4x=x+12|-x\\3x=12|:3\\x=4$

Succes! :)