Question

Rezolvati in R ecuatia:
a) (x-1)^2+(x+2)^2-(x-2)(x+2)=24
b) (x-2)^2+(x+1)^2-(x-1)(x+1)=14

Answer 1

a. (x-1)²+(x+2)²-(x-2)(x+2)=24
x²-2x+1+x²+4x+4-x²+4=24
x²+2x+9=24
x²+2x-15=0
Δ=4-4x1x(-15)=64, √Δ=8
x1=(-2+8)/2=3, x2=(-2-8)/2=-5
b. x²-4x+4+x²+2x+1-x²+1=14
x²-2x+6=14
x²-2x-8=0
Δ=4-4x1x(-8)=4+32=36, √Δ=6
x1=(2+6)/2=4, x2=(2-6)/2=-2