382
1) (x+5)^2-x^2=x-2
x^2+10x+25-x^2-x+2=0
9x+27=0
x=-3
2) (6-x)^2-16=x^2-2x
36-12x+x^2-16-x^2+2x=0
-10x+20=0
-10x=-20
10x=20
x=2
3) (3x+1)^2-(3x-1)^2=x+5
9x^2+6x+1-(9x^2-6x+1)-x-5=0
6x+6x-x-5=0
11x-5=0
11x=5
x=5/11
4) (2y-1)^3+(2y+1)^3=y(1+16y^2)+2
(2y-1)(2y-1)^2+(2y+1)(2y+1)^2=y(1+16y^2)+2
8y^3-8y^2+2y-4y^2+4y-1+(2y+1)(4y^2+4y+1)=y(1+16y^2)+2
8y^3-12y^2-6y+1+(8y^3+8y^2+2y+4y^2+4y+1=y(1+16y^2)+2
8y^3+6y+1+8y^3+6y+1=y(1+16y^2)+2
16y^3+12y+2=y(1+16y^2)+2
16y^2+12y+2=y+16y^3+2
16y^3+12y+2-y-16y^3-2=0
12y-y=0
11y=0
y=0
383
1) a^2+a/a^2-1=abx/ab-b
(a^2+a)(ab-b)=(a^2-1)(abx)
a^3b-ba^2+ba^2-ab=a^3bx-abx
a^3b-ab=a^3bx-abx
x(a^3b-ab)=a^3b-ab
x=a^3b-ab/a^3b-ab
x=1
2) 6a^3-6/a^2+a+1=(a-1)x/18
18(6a^3-6)=(a^2+a+1)(a-1)x
(a^3-1)x=108a^3-108
x=108a^3-108/a^3-1
x=108(a^3-1)/a^3-1
x=108
3) ab+3/21b^3+21=7x/5b^2-5b+5
49x(b^3+1)=(b+1)(5b^2-6b+5)
49x(b^3+1)=5b^3-5b^2+5b+5b^2-5b+5
49x(b^3+1)=5b^3+5
49x(b^3+1)=5(b^3+1)
49x=5
x=5/49
4) a^2b-a/1-a^2b^2=6ax/18+18ab
a^2b-a/1-a^2b^2=6ax/18(1+ab)
a^2b-a/1-a^2b^2=ax/3(1+ab)
ax(1-a^2b^2)=3(1+ab)(a^2b-a)
x(a-a^3b^2)=3(a^2b-a+a^3b^3-a^2b)
x=3(a^3b^3-a)/a-a^3b^2