Question

Rozwiąż równanie.

a) y(2y-1) = 2(2+y)²

b) (1/2x-4)² = (1/2x+4)²

c)(√3y+2)² - (√ 3y+2)(√ 3y-2) = 0

d) 5x²+2 = (x-3)²

Dam naaaj.

Answer 1

a) y(2y-1) = 2(2+y)²

2y² - y = 2 ( 4 + 4y + y²)

2y² - y = 8 + 8y + 2 y²

9y + 8 = 0

y = -8/9

b) (1/2x-4)² = (1/2x+4)²

1/4x² - 4x + 16 = 1/4x² + 4x + 16

4x + 16 = -4x + 16

-4x = 4x

x = 0

c)(√3y+2)² - (√ 3y+2)(√ 3y-2) = 0

3y² + 4√3y + 4 -  3y² - 2√3y + 2√3y - 4 = 0

4√3y + 4  = 0

√3y + 1 = 0

√3y = -1

y = -1/√3

y = -√3/3

 

d) 5x²+2 = (x-3)²

5x² + 2 = x² - 6x + 9

4x² = -6x + 7

4x² + 6x - 7 = 0

Δ = 36 + 112 = 148

√Δ = 2√37

x₁ = -6 - 2√37 / 8 

x₂ = - 6 + 2√37 / 8