Question

3 Równiania kwadratowe:
(x - 2 ) ( x+2 ) = 4
x(x-2)=x^+5
(x-2)^-3(x-2)=2x^-3-7x

Answer 1

(x - 2 ) ( x+2 ) = 4
x²-4 = 4
x²-4-4 = 0
x²-8 = 0
Δ = b² - 4ac = 0 - 4 * 1 * (-8) = 0+32 = 32 ; √Δ = √32 = 4√2
x₁ = -b-√Δ / 2a = 0-4√2 / 2 =-4√2 / 2 = -2√2
x₂ = 0+4√2 / 2 = 4√2 / 2 = 2√2

x(x-2)=x²+5
x²-2x = x² + 5
x²-x² - 2x = 5
-2x = 5 /:(-2)
x = -5/2

(x-2)²-3(x-2)=2x²-3-7x
x²-4x+4-3x+6 = 2x²-7x-3
x²-2x²-4x-3x+7x = -3-6-4
-x² +13 = 0
Δ = b² - 4ac = 0 - 4*(-1)*13 = 0 + 52 = 52 ; √Δ = √52 = 2√13
x₁ = -b-√Δ / 2a = 0-2√13 / -2 = -2√13/-2 =√13
x₂ = 0+2√13 / -2 = 2√13 /-2 = -√13

Answer 2

3 Równiania kwadratowe: (x - 2 ) ( x+2 ) = 4 x(x-2)=x^+5 (x-2)^-3(x-2)=2x^-3-7x