a: =>\(\sqrt[3]{x-2}-1+\sqrt{x+1}-2=0\)
=>\(\dfrac{x-2-1}{\sqrt[3]{\left(x-2\right)^2}+\sqrt[3]{\left(x-2\right)}+1}+\dfrac{x+1-4}{\sqrt{x+1}+2}=0\)
=>x-3=0
=>x=3
c: =>(x+1)^2=(x-3)^3
=>x^3-9x^2+27x-27-x^2-2x-1=0
=>x^3-10x^2+25x-28=0
=>x^3-7x^2-3x^2+21x^2+4x-28=0
=>(x-7)(x^2-3x+4)=0
=>x=7