b: \(\left(x^2-4x\right)^2+2\left(x-2\right)^2=43\)
=>\(\left\lbrack\left(x^2-4x+4\right)-4\right\rbrack^2+2\left(x-2\right)^2=43\)
=>\(\left\lbrack\left(x-2\right)^2-4\right\rbrack^2+2\left(x-2\right)^2=43\)
=>\(\left(x-2\right)^4-8\left(x-2\right)^2+16+2\left(x-2\right)^2-43=0\)
=>\(\left(x-2\right)^4-6\left(x-2\right)^2-27=0\)
=>\(\left\lbrack\left(x-2\right)^2-9\right\rbrack\left\lbrack\left(x-2\right)^2+3\right\rbrack=0\)
=>\(\left(x-2\right)^2-9=0\)
=>(x-2-3)(x-2+3)=0
=>(x-5)(x+1)=0
=>x=5 hoặc x=-1
c: \(\left(x^2+x\right)^2+4\left(x^2+x\right)=12\)
=>\(\left(x^2+x\right)^2+4\left(x^2+x\right)-12=0\)
=>\(\left(x^2+x+6\right)\left(x^2+x-2\right)=0\)
=>\(x^2+x-2=0\)
=>(x+2)(x-1)=0
=>x=-2 hoặc x=1
d: x(x-1)(x+1)(x+2)=24
=>\(\left(x^2+x\right)\left(x^2+x-2\right)=24\)
=>\(\left(x^2+x\right)^2-2\left(x^2+x\right)-24=0\)
=>\(\left(x^2+x-6\right)\left(x^2+x+4\right)=0\)
=>\(x^2+x-6=0\)
=>(x+3)(x-2)=0
=>x=-3 hoặc x=2
