Question

Rozwiaz równania
a) 1-x^2=1-x

b) 4-x=1/x x^2+4

c) 1-6x=-9x^2

d) x^2=12x -36

e) x(x+1)=9x-16

f) 1/2x(6-x)=2+x

Answer 1

a) 1-x^2=1-x
-x²+x=0
-x(x-1)=0
x=0 x=1

b) 4-x=1/x x^2+4
-x²-1/2x=0
-x(x+1/2)=0
x=0 x=-1/2

c) 1-6x=-9x^2
9x²-6x+1=0
Δ=36-36=0 x0=6/18=1/3

d) x^2=12x -36
x²-12x+36=0
Δ=144-144=0 x0=12/2=6

e) x(x+1)=9x-16
x²+x-9x+16=0
x²-8x+16=0
Δ=64-64=0 x0=8/2=4

f) 1/2x(6-x)=2+x
3x-1/2x²-2-x=0
1/2x²+2x-2=0
Δ=4-4=0 x0=-2/1=-2