Question

rezolvati in multimea nrelor reale ecuatia

2 - radical din 2-x=x

Answer 1

2-√(2-x)=x
-√(2-x)=x-2    inmultim-1
√(2-x)=2-x
(√(2-x)²=(2-x)²
2-x=4-4x+x²
-x²+4x-x-4+2=0
-x²+3x-2=0      inmultim -1
x²-3x+2=0
Δ=9-8=1
x₁=(3-1)/2=1
x₂=(3+1)/2=2
x∈{1,2}