Question

vreau rezolvarea detaliat caci stiu rsp. Aduceti la forma cea mai simpla expresia:

a) -(a-5)(a+3)-(1-a)^2 = -2a^2+4a-16

B) (x-1)(x-2)-(x-4)^2 = 5x-14

c) (2a+0,5)^2-(0,5-2a)^2 = 4a

Answer 1

a) −(a−5)(a+3)−(1−a)²=−2a²+4a−16
−a²+4a+13=−2a²+4a−16
−a²+4a+13+2a²=−2a²+4a−16+2a²
a²+4a+13=4a−16
a²+4a+13−4a=4a−16−4a
a²+13=−16
a²+13−13=−16−13
a²=−29
a=±√−29

b) (x−1)(x−2)−(x−4)²=5x−14
x²−5x+10=5x−14
x²−5x+10−(5x−14)=5x−14−(5x−14)
x²−10x+24=0
(x−4)(x−6)=0
x−4=0 or x−6=0x=4 or x=6

c) (2a+0.5)²−(0.5−2a)²=4a
4a²+2a+0.25+−4a²+2a+−0.25=4a
(4a²+−4a²)+(2a+2a)+(0.25+−0.25)=4a
4a=4a
4a−4a=4a−4a0=0