Question

Rezolvati ecuatile,dau 30 de puncte,va rog.

Answer 1

a) (x+2)² = 10x-4
x²+4x+4 = 10x -4
x²-6x+8 = 0 =>Δ=b²-4ac => Δ= 36-32 => Δ=4
x₁=(-b+√Δ)/2a => x₁ = (6+√4)/2 => x₁ = 8/2 => x₁ = 4
x₂=(-b-√Δ)/2a => x₂ = (6-√4)/2 => x₂ = 4/2 => x₂ = 2

b) (3x-2)² = 4x-3
9x² - 12x +4 = 4x-3
9x² - 16x +7 = 0 => Δ=b²-4ac => Δ= 256- 252=> Δ=4
x₁=(-b+√Δ)/2a => x₁ = (16+√4)/2 => x₁ = 18/2 => x₁ = 9
x₂=(-b-√Δ)/2a => x₂ = (16-√4)/2 => x₂ = 14/2 => x₂ = 7

c) (4x-1)² = x+1
16x² - 8x + 1 = x+1
16x² - 9x + 0 = 0 => Δ=b²-4ac => Δ= 81
x₁=(-b+√Δ)/2a => x₁ = (9+√81)/2 => x₁ = 18/2 => x₁ = 9
x₂=(-b-√Δ)/2a => x₂ = (9-√81)/2 => x₂ = 0/2 => x₂ = 0

d) (x+2)² + (x-1)² = 6x+3
x²+4x+4 + x²-2x+1 = 6x+3
2x²-4x+2=0 => Δ=b²-4ac => Δ= 16-16 => Δ=0 =>
=> Δ=0 => x₁=x₂ =  \frac{-b}{a} => x= 4/2 = 2

e) (4x-3)² = 7x-6 (Aici ai gresit tu cand ai scris cred)
16x² -24x + 9 = 7x-6
16x² -31x +15 = 0 => Δ=b²-4ac => Δ= 961-960 => Δ=1
x₁=(-b+√Δ)/2a => x₁ = (31+1)/2 => x₁ = 32/2 => x₁ = 16
x₂=(-b-√Δ)/2a => x₂ = (31-1)/2 => x₂ = 30/2 => x₂ = 15

f) (3x+2)² = 5x+4
9x²+12x+4 = 5x+4
9x²+7x+0 = 0 => Δ=b²-4ac => Δ= 49
x₁=(-b+√Δ)/2a => x₁ = (-7+7)/2 => x₁ = 0/2 => x₁ = 0
x₂=(-b-√Δ)/2a => x₂ = (-7-7)/2 => x₂ = -14/2 => x₂ = -7

a) (3x+y)² = 3x²+6xy+y²

b) (2x+5y)² = 4x²+20xy+25y²

c) (x+4y)² = x²+8xy+16y²

d) (3x-4y)² = 9x²-24xy+16y²

e) (x-y)² + (x+2y)² = x²-2xy+y² + x²+4xy+4y² = 2x²+2xy+5y²

f) (x+5)² + (x-3)² = x²+10x+25 + x²-6x+9 = 2x²+4x+36

g) (2x-1)² + (3x-1)² = 4x²-4x+1 + 9x² -6x +1 = 13x² -10x +2

h) (4x-2)² + (2x-1)² = 16x² -16x +4 + 4x² -4x +1 = 20x²-12x+5

Sper ca te-am ajutat.
Mult noroc la scoala :D