Question

Lectia -Ecuatii de forma x²=a.a∈Q
2.Rezolvati in R ecuatiile :
j) (x+1)²=1,(7)
i) $\frac{5}{x-1} = \frac{x-1}{45}$

Answer 1

1,(7)=(17-1)/9=16/9
x²+2x+1=16/9
9(x²+2x+1)=16
9x²+18x+9-16=0
9x²+18x-7=0
Δ=324+252=576
x1=(-18+24)/18=6/18=1/3
x2=(-18-24)/18=-42/18=21/9=7/3
x∈{1/3,7/3}

i)45·5=(x-1)(x-1)
225=x²-2x+1
-x²+2x-1+225=0
-x²+2x+224=0    inmultim -1
x²-2x-224=0
Δ=4+896=900
x1=(2-30)/2=-28/2=-14
x2=(2+30)/2=32/2=16
x∈{-14,16}