Question

Rezolvati in multimea numerelor reale,ecuatia:
(x-1)²-(x-2)²=4x-5

Answer 1

x²-2x+1-(x²-4x+4)=4x-5
x²-2x+1-x²+4x-4=4x-5
2x-3=4x-5
4x-2x-5+3=0
2x-2=0
2x=2
x=1
Spor la lucru!

Answer 2

$\displaystyle (x-1)^2-(x-2)^2=4x-5 \\ x^2-2 \cdot x \cdot 1+1^2-(x^2-2 \cdot x \cdot 2+2^2)=4x-5 \\ x^2-2x+1-(x^2-4x+4)=4x-5 \\ x^2-2x+1-x^2+4x-4=4x-5 \\ x^2-2x-x^2+4x-4x=-5-1+4 \\ -2x=-2 \\ x= \frac{-2}{-2} \\ x=1$