Question

Ex 20 va rog, doar cine stie foarte bine sa le faca, dau coroana!

Answer 1

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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