Question

Rozwiąż równanie:
a)(2x-3) (2x+3)=(x+5)²-9
b)x²-(3x-1)²=56x-43
c)3(x+1)(x-2)=2x²-x-7
d)17-5x=6x²+(x-x)²
e)11-14x=(2x+1)²
f)6x²=x+1
g)5x²=2-9x

Answer 1

A)(2x-3) (2x+3)=(x+5)²-9
4x²-9=x²+10x+25-9
4x²=x²+10x+25
3x²-10x-25=0
Δ=(-10)²-4*3*(-25)=100+300=400
√Δ=20
x1=10+20/6=30/6=5
x2=10-20/6=-10/6=-1 i 2/3

b)x²-(3x-1)²=56x-43
x²-9x²+6x-1=56x-43
-8x²+6x-1=56x-43
-8x²-50x+42=0
Δ=(-50)²-4*(-8)*42=2500+1344=3844
√Δ=62
x1=50+60/-16=110/-16=-6 i 7.8
x2=50-60/-16=-10/-16=5/8

c)3(x+1)(x-2)=2x²-x-7
3(x²-2x+x-2)=2x²-x-7
3(x²-x-2)=2x²-x-7
3x²-3x-6=2x²-x-7
x²-2x+1=0
Δ=(-2)²-4*1*1=4-4=0
x=3/6=1/2

d)17-5x=6x²+(x-x)²
17-5x=6x²+x²-2x²+x²
17-5x=6x²
-6x²-5x+17=0
Δ=(-5)²-4*(-6)*17=25+408=433
√Δ=√433
x1=5+√433/-12
x2=5-√433/-12

e)11-14x=(2x+1)²
11-14x=4x²+4x+1
-4x²-18x+10=0
Δ=(-18)²-4*(-4)*10=324+160=484
√Δ=22
x1=18+22/-8=40/-8=-5
x2=18-22/-8=-4/-8=1/2

f)6x²=x+1
6x²-x-1=0
Δ=(-1)²-4*6*(-1)-1+24=25
√Δ=5
x1=1+5/12=6/12=1/2
x2=1-4/12=-3/12=-1/4


g)5x²=2-9x
5x²+9x-2=0
Δ=9²-4*5*(-2)=81+40=121
√Δ=11
x1=-9-11/10=-20/10=-2
x2=-9+11/10=2/10=1/5

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