Question

rezolvati ecuatia (x-2)(x+1)(x+4)(x+7)=40​

Answer 1

(x-2)(x+1)(x+4)(x+7)=40

(x-2) (x+7)(x+1)(x+4)=40

(x²+5x-14)( x²+5x+4)=40

notam y= x²+5x

=> (y-14)(y+4)=40

y²-10y-56=40

y²-10y-96=0

Δ=100+384=484

y1=(10+22)/2=16  si y1=(10-22)/2= -6

x²+5x=16

x²+5x-16=0; Δ=25+64=89

x1=(-5+√89)/2

x2=(-5-√89)/2

x²+5x=-6

x²+5x+6=0

d=25-24

x3=(-5+1)/2= -2

x4=(-5-1)/2= -3

Solutii rationale: -2 si -3