Question

Rozwiąż równanie:
a)(3x-1)(4x+5)=(4x+5)(2x-1)
b)51-y(3y+4)=2(17-2y)-58
c)(2+5x)²=19x+(x-4)(x+5)
d)25(x-1)²-9(x+2)²=0
e)3x²-2√3x-3=0
f)(x+3)²-5(x+3)+4=0

Answer 1

A)(3x-1)(4x+5)=(4x+5)(2x-1)
12x²+15x -4x-5=8x²-4x-5+10x
4x²+5x=0
Δ=25-16=9
√Δ=3
x₁=-5-3/8=-1
x₂=-5+3/8=-1/4
b)51-y(3y+4)=2(17-2y)-58
51-3y²-4y=34-4y-58
-3y²=-75
y²=25
y=5 lub y=-5
c)(2+5x)²=19x+(x-4)(x+5)
4+20x+25x²=19x+x²+5x-4x-20
24x²=-24
x²= -1 sprzecznosc
d)25(x-1)²-9(x+2)²=0
25(x²-2x+1)-9(x²+4x+4)=0
25x²-50x+25-9x²-36x-36=0
16x²-86x-11=0
Δ=(-86)²-4×(-11)×16=7396+704=8100
√Δ=90
x₁=86-90/32=-4/32=-1/8
x₂=86+90/32=176/32=5,5
e)3x²-2√3x-3=0
f)(x+3)²-5(x+3)+4=0
x²+6x+9-5x-15+4=0
x²+x-2=0
Δ=1+8=9
√Δ=3
x₁=-1-3/2=-2
x₂=-1+3/2=1