Question

8)Rezolvati in R ecuatiile:
a)x²-2x-3=0
b)x²-6x+5=0
c)x²-3x+2=0
d)x²-8x+16=0
e)x²-7x+12=0
f)x²+2x-35=0

Answer 1

a)Δ=2²-4·1·3⇒Δ=-8
x1=-2-√8 supra 2·1⇒x1=2+2√2 supra 2 ⇒2√2
x2=(-2)+√8 supra 2·1⇒x2=-2√2
b)Δ=6²-4·1·5⇒Δ=16
x1=-6-√16 supra 2·1⇒x1=⇒5
x2=-6+√16 supra 2⇒x2⇒-1
c)Δ=3²-4·1·2⇒Δ=1
x1=-3-√1 supra 2⇒x1=-2
x2=-3+√1supra 2⇒x2=-1
d)Δ=8²-4·1·16⇒Δ=0
ecuatiile nu au sens
e)Δ=7²-4·1·12⇒Δ=1
x1=-7-√1 supra 2⇒x1=4
x2=-7+√1 supra 2⇒x2=-3

Answer 2

astea sunt ecuatii cu delta
a)x²-2x-3=0
Δ=b²-4ac⇒Δ=(-2)²-4×1×(-3)=4-4×(-3)=4+12=16
x1=-b+√Δ/2a⇒x1=-(-2)+√16/2×1=2+4/4=6/2=3
x2=-b-√Δ/2a=-(-2)-√16/2×1=2-4/2=-2/2=-1
b)x²-6x+5=0
Δ=b²-4ac⇒Δ=(-6)²-4×1×4=36-4×5=36-20=16
x1=-b+√Δ/2a⇒x1=-(-6)+√16/2×1=6+4/2=10/2=5
x2=-b-√Δ/2a⇒x2=-(-6)-√16/2×1=6-4/2=2/2=1
c)x²-3x+2=0
Δ=b²-4ac⇒Δ=(-3)²-4×1×2=9-8=1
x1=-b+√Δ/2a⇒x1=-(-3)+√1/2×1=3+1/2=4/2=2
x2=-b-√Δ/2a⇒x2=-(-3)-√1/2×1=3-1/2=2/2=1
d)x²-8x+16=0
Δ=b²-4ac⇒Δ=(-8)²-4×1×16⇒Δ=64-64⇒Δ=0
x1=x2=-b/2a=-(-8)/2×1=8/2=4
e)x²-7x+12=0
Δ=b²-4ac⇒Δ=(-7)²-4×1×12⇒Δ=49-48⇒Δ=1
x1=-b+√Δ/2a⇒x1=-(-7)+√1/2×1=7+1/2=8/2=4
x2=-b-√Δ/2a⇒x2=-(-7)-√1/2×1=7-1/2=6/2=3
f)x²+2x-35=0
Δ=b²-4ac⇒Δ=2²-4×1×(-35)=4-4×(-35)=4+140=144
x1=-b+√Δ/2a⇒x1=-2+√144/2×1⇒x1=-2+12/2=10/2=5
x2=-b-√Δ/2a⇒x2=-2-√144/2×1=-2-12/2=-14/2=-7