Question

Uporządkuj i rozwiąż równanie:


A) (x+1)kwadrat =2x+10
B) (x-1)kwadrat =26-2x
C) (x+1)kwadrat +(x-1)kwadrat =20
D) (x+3)kwadrat=50 -(x-3)kwadrat

Answer 1

A) (x+1)kwadrat =2x+10
x²+2x+1=2x+10
x²-9=0
(x+3)(x-3)=0
x1=-3
x2=3
B) (x-1)kwadrat =26-2x
x²-2x+1=-2x+26
x²-25=0
(x-5)(x+5)=0
x1=5
x2=-5
C) (x+1)kwadrat +(x-1)kwadrat =20
x²+2x+1+(x²-2x+1)=20
2x²+2-20=0
2x²-18=0
Δ=b²-4*a*c=0-4*2*(-18)=-8*(-18)=144
√Δ=12
x1=-12/4=-3
x2=12/4=3
D) (x+3)kwadrat=50 -(x-3)kwadrat
x²+6x+9=50-(x²-6x+9)
x²+6x+9=50-x²+6x-9
x²+6x+9-50+x²-6x+9=0
2x²+18-50=0
2x²-32=0
Δ=b²-4*a*c=0-4*2*(-32)=-8*(-32)=256
√Δ=16
x1=-16/4=-4
x2=16/4=4