Question

Ecuatie irationala:
$\sqrt{x+ \sqrt{x+2} }+ \sqrt{x- \sqrt{x+2} } =2$

Macar o indicatie.

Answer 1

x+√x+2+2√x²-x-2+x-√x+2=4
2x+2√x²-x-2=4
x+√x²-x-2=2
√x²-x-2=2-x
(√x²-x-2)²=(2-x)²
x²-x-2=4-4x+x²
x²-x-2-4+4x-x²=0
3x-6=0
3x=6
x=2

Answer 2

Ridica la a 2 a si in stanga si in drapta ca sa scapi de radical si vine
x+ √x+2 +x -√x+2 + 2√(x+√x+2)(x- √x+2) =4
In membrul stang ai o simplificare √x+2-√x+2 si folosesti pentru radical formula a*a +b*b= (a+b)(a-b)
Apoi ridici din nou la patrat si folosesti formula (a+b) la a 2 a= a la a 2 a +2ab+ b la a 2 a