Răspuns:
Explicație pas cu pas:
Aplicand formulele:
(a+b)²=a²+2ab+b²
(a-b)²=a²-2ab+b²
a²-b²=(a+b)(a-b)
vom rezolva in felul urmator
a) (x+2)²-(x+3)²=9(x-1)-4(3x-2)-6
x²+4x+4-(x²+6x+9)=9x-9-12x+8-6
x²+4x+4-x²-6x-9=9x-9-12x+8-6
-2x-5=-3x-7
3x-2x=5-7
x= - 2
b) (x+2)²-(x+1)²+5=2(x-3)+(x+3)-2
x²+4x+4-x²-2x-1+5=2x-6+x+3-2
2x+8=3x-5
3x-2x=8+5
x=13
c) (x-1)²-(2x+1)²-6=2(5-x)-3x(x+1)-23
x²-2x+1-4x²-4x-1-6=10-2x-3x²-3x-23
-3x²-6x-6=-3x²-5x-13
-3x²-6x+3x²+5x=-13+6
-x=-7
x=7
d) (x+3)²-(x-2)²+12=2(4x+1)+3(x+5)-3
x²+6x+9-x²+4x-4+12=8x+2+3x+15-3
10x+17=11x+14
11x-10x=17-14
x=3
e) (2x+1)²-2(x+4)=(2x-1)²+3(x+2)+7
4x²+4x+1-2x-8=4x²-4x+1+3x+6+7
4x²+2x-7=4x²-x+14
4x²+2x-4x²+x=14+7
3x=21
x=21:3
x=7
f) (x+5)²+(x-6) (x+6)=2(x+3)²+15
x²+10x+25+x²-36=2(x²+6x+9)+15
2x²+10x-11=2x²+12x+18+15
2x²+10x-2x²-12x=33+11
-2x=44
x=-44:2
x=-22
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