Question

Rezolvati in R ecuatia:

a) x²-4x=12
b)4x²+12x=16
c)9x²-6x=120
d)x²+10x=24

Answer 1

a) x²-4x=12
x²-4x-12=0
Δ=b²-4ac=(-4)²-4x1x(-12)=16-4x(-12)=16+48=64
x₁=-b+√Δ/2a=-(-4)+√64/2x1=4+8/2=12/2=6
x₂=-b-√Δ/2a=-(-4)-√64/2x1=4-8/2=-4/2=-2
b)4x²+12x=16
4x²+12x-16=0
Δ=b²-4ac=12²-4x4x(-16)=144+256=400
x1=-b+√Δ/2a=-(12)+√400/2x4=-12+20/2x4=8/8=1
x2=-b-√Δ/2a=-(12)-√400/2x4=-12-20/8=-32/8=-4
c)9x²-6x=120
9x²-6x-120=0
Δ=b²-4ac=(-6)²-4x9x(-120)=36-36x(-120)=36-(-4320)=4356
x1=-b+√Δ/2a=-(-6)+√4356/2x9=6+66/2x9=72/18=4
x2=-b-√Δ/2a=-(-6)-√4356/2x9=6-66/2x9=-60/18=simplific cu 3=-20/6 simplific cu 2=-10/3
d)x²+10x=24
x²+10x-24=0
Δ=b²-4ac=10²-4x1x(-24)=100-4x(-24)=100-(-96)=100+96=196
x1=-b+√Δ/2a=-10+√196/2x1=-10+14/2=-4/2=-2
x1=-b-√Δ/2a=-10-√196/2=-10-14/42=-24/2=-12