Question

2x²- 3=(5х -4)(2х-3) 2) (2х - 1)(2х + 3)- (х-2)(х + 2)=21​

Answer 1

1) 2x²-3 = (5х-4)(2х-3)
2x²-3 = 10x²-15x-8x+12
10x²-2x²-23x+12+3 = 0
8x²-23x+15 = 0
D = (-23)²-4*8*15 = 529-480 = 49 = 7²
x₁₂ = (23±7)/(2*8)
x₁ = 30/16 = 15/8 = 1,875 ; x₂ = 16/16 = 1

2) (2х-1)(2х+3)-(х-2)(х+2) = 21​
4x²+6x-2x-3-(x²-4)-21 = 0
4x²-x²+4x-24+4 = 0
3x²+4x-20 = 0
D = 4²-4*3*(-20) = 16+240 = 256 = 16²
x₁₂ = (-4±16)/(2*3)
x₁ = 12/6 = 2 ; x₂ = -20/6 = -10/3 = -3,(3)