Найдите произведение корней уравнения 2√x²-x-1-√x²-x-2=2

ОДЗ

x²-x-1≥0

D=1+4=5

x1 = (1-√5) / 2 U x2 = (1+√5) / 2

x≤ (1-√5) / 2 U x≥ (1+√5) / 2

x²-x-2≥0

x1+x2=1 U x1*x2=-2⇒x1=-1 U x2=2

x≤-1 U x≥2

x∈ (-∞; -1] U [2; ∞)

2√ (x²-x-1) = 2+√ (x²-x-2)

4 (x²-x-1) = 4+4√ (x²-x-2) + x²-x-2

4x²-4x-4-x²+x-2=4√ (x²-x-2)

3x²-3x-6=4√ (x²-x-2)

3 (x²-x-2) = 4√ (x²-x=2)

√ (x²-x-2) = a

3a²=4a

3a²-4a=0

a (3a-4) = 0

a=0⇒√ (x²-x-2) = 0

x²-x-2=0

x=-1 U x=2

a=4/3⇒√ (x²-x-2) = 4/3

x²-x-2=16/9

9x²-9x-18=16

9x²-9x-34=0

D=81+1224=1305

√D=3√145

x1 = (9-3√145) / 18=1/2-√145/6

x2=1/2+√145/6