Question

Aflați soluțiile ecuațiilor:
a) 3(x+5)-5(1-x)(1+x)=(x-3)^2+(2x-1)^2+13
b) (x-3)(2-x)-(x-5)(5+x)=-2x(x-6)-5(x-1)
c) 3(1-x)^2-4(x-2)^2+5(x-3)^2=(2x-3)^2+4-x
d) x(1-x)+(2-x)^2+(3+x)^2-1=(x-1)(4-x)+(2x+1)(2+x)
Trebuie să dea: 1;7; 19 supra 7 şi 2

Answer 1

a. 3x+15-5(1-x²)=x²-6x+9+4x²-4x+1+13
3x+15-5+5x²=5x²-10x+23
3x+10=-10x+23
-13x=-13, x=1

b. 2x-x²-6+3x-x²+25=-2x²+12x-5x+5
5x+19=7x+5
5x-7x=-19+5
-2x=-14, x=7

c. 3(1-2x+x²)-4(x²-4x+4)+5(x²-6x+9)=4x²-12x+9+4-x
3-6x+3x²-4x²+16x-16+5x²-30x+45=4x²-13x+13
-20x+32=-13x+13
-7x=-19, x=19/7

d. x-x²+4-4x+x²+9+6x+x²-1=4x-x²-4+x+4x+2x²+2+x
3x+12=10x-2
-7x=-14
x=2