Question

3 Rezolvați ecuația (x + 1)² - 5x² = 2(x - 3)²-(x + 2)².​

Answer 1

(x+1)^2-5x^2=2(x-3)^2-(x+2)^2
x^2+2x+1-5x^2=2(x^2-6x+9)-(x^2+4x+4)
-4x^2+2x+1=2x^2-12x+18-x^2-4x-4
-4x^2+2x+1-2x^2+12x-18+x^2+4x+4=0
-5x^2+18x-13=0
Delta=324-260=64
Radical din delta=8
x1=-18-8/-10=-26/-10=13/5
x2=-18+8/-10=-10/-10=1
Deci x=1

Answer 2

Răspuns:

x₁ = 1 ; x₂ = 13/5

Explicație pas cu pas:

(x+1)²-5x² = 2(x-3)²-(x+2)² <=>

x²+2x+1-5x² = 2(x²-6x+9)-(x²+4x+4) =>

-4x²+2x+1 = 2x²-12x+18-x²-4x-4 =>

x²+4x²-16x-2x+14-1 = 0 =>

5x²-18x+13 = 0 <=>

5x²-5x-13x+13 = 0 <=>

5x(x-1) - 13(x-1) = 0 <=>

(x-1)(5x-13) = 0 =>

x₁ = 1 ; x₂ = 13/5