Question

solutiile reale ale ecuatiei
$x {}^{2} - \sqrt{12} = \sqrt{(2 \sqrt{3} - 4) {}^{2} }$

Answer 1

Ecuatia devine x²-√12=|2√3-4|

Dar |2√3-4| =4-2√3 deoarece 2√3<4

Atunci ecuatia va fi: x²-2√3=4-2√3⇒x²=4⇒x1=2, x2=-2, x∈{-2,2}

Answer 2

x²-√12=√(2√3-4)²

x²-√12=|2√3-4|

x²-√12=4-2√3

x²-2√3=4-2√3

x²-4=0

(x-2)(x+2)=0

x₁-2=0⇒x₁=2;

x₂+2=0⇒x₂=-2;

x∈{-2;2}

Raspuns: S={-2;2}.

Bafta!