Question

Simplificati raportul: 4x pătrat+3x-1 totul supra 4x pătrat -5x+1.

Answer 1

4x²+3x-1=0
a=4 b=3 c=-1
∆=b²-4ac
∆=3²-4•4•(-1)
∆=9+16
∆=25=>√∆=√25=5
x1=(-b+√∆)/2a=-3+5/2•4
=2/2•4=1/4
x2=(-b-√∆)/2a=-3-5/2•4
x2=-8/8=-1
Voi aplica formula
ax²+bx+c=a(x-x1)(x-x2) 4x²+3x-1=4(x-1/4)(x-(-1))
=(4x-1)(x+1)

4x²-5x+1=0
a=4 b=-5 c=1
∆=b²-4ac
∆=(-5)²-4•4•1
∆=25-16
∆=9=>√∆=√9=3
x1=(-b-√∆)/2a
x1=5-3/2•4=2/2•4=1/4
x2=(-b+√∆)/2a
x2=5+3/2•4=8/8=1
Voi aplica formula
ax²+bx+c=a(x-x1)(x-x2)
4x²-5x+1=4(x-1/4)(x-1)
=(4x-1)(x-1)

(4x²+3x-1)/(4x²-5x+1)=
=(4x-1)(x+1)/(4x-1)(x-1)
Voi simplifica prin 4x-1 și raportul x+1/x-1
Deci vei obtine x+1/x-1