Odpowiedź:
Szczegółowe wyjaśnienie:
a) 1/3 x² + 1/4x = x - 1 |*12
4x² +3x = 12x -12
4x² -9x + 12 = 0
Δ <0
x∈∅
b) (3-x²)(7+x²)=0
3-x²= 0 ∨ 7+x² = 0
x = √3 ∨ x = -√3 ∨ x∈∅
x∈{-√3, √3}
c) (5x-1)² = (3x+2)²
25x² - 10x + 1 = 9x² +12x + 4
16x² - 22x - 3 = 0
Δ = 484 + 192 = 676
√Δ = 26
x1 = 22+26/16 = 3 ∨ x2 = -1/4
x∈ { -1/4, 3}
d) x-3/2 = (2x-1)(2x+1)
x-3/2 = 4x²-1
x-3 = 8x² - 2
8x² - x + 1 = 0
Δ = 1 -33 = -32
x∈∅
