Równanie do rozwiązania

[Glazzz]

Jak rozwiązać:
a. \(\displaystyle{ (1-2x) ^{2} -(1-2x)(x ^{2} +3)=0}\)
b. \(\displaystyle{ (x-3)(2x+2)=(x-3)(x ^{2} -6)}\)
c. \(\displaystyle{ x ^{2} (2x-3)(x+2)=x ^{3} -2x ^{2}}\)

[tometomek91]

a)
\(\displaystyle{ (1-2x) ^{2} -(1-2x)(x ^{2} +3)=0\\
(1-2x)[(1-2x)-(x ^{2} +3)]=0\\
(1-2x)(1-2x-x^{2}-3)=0\\
1-2x=0 \vee x^{2}+2x+2=0\\
...}\)

b)
\(\displaystyle{ (x-3)(2x+2)=(x-3)(x ^{2} -6)\\
(x-3)(2x+2)-(x-3)(x ^{2} -6)=0\\
(x-3)[(2x+2)-(x ^{2} -6)]=0\\
(x-3)(x^{2}-2x-8)=0\\
(x-3)(x-4)(x+2)=0\\
...}\)

c)
\(\displaystyle{ x ^{2} (2x-3)(x+2)=x ^{3} -2x ^{2}\\
x ^{2} (2x-3)(x+2)=x^{2}(x-2)\\
x ^{2} (2x-3)(x+2)-x^{2}(x-2)=0\\
x^{2}[(2x-3)(x+2)-(x-2)]=0\\
x^{2}(2x^{2}-4)=0\\
...}\)

[Glazzz]

I jeszcze jak rozłożyć na czynniki:
a. \(\displaystyle{ (x-1) ^{2} -(x+1) ^{2}}\)
b. \(\displaystyle{ 9x ^{2} (x+2) ^{2} -x ^{2}}\)
c. \(\displaystyle{ (2x+1) ^{2} -2(2x+1)+1}\)
d. \(\displaystyle{ (9x ^{2} -12x+4)(3x ^{2} -4x+4)}\)