b: \(\left(x^2-3x+2\right)\left(x^2-12x+32\right)\le4x^2\)

=>(x-1)(x-2)(x-4)(x-8)<=\(4x^2\)

=>\(\left(x^2-9x+8\right)\left(x^2-6x+8\right)\le4x^2\)

=>\(\left(x^2+8\right)^2-15x\left(x^2+8\right)+54x^2-4x^2\le0\)

=>\(\left(x^2+8\right)^2-15x\left(x^2+8\right)+50x^2\le0\)

=>\(\left(x^2-5x+8\right)\left(x^2-10x+8\right)\le0\)

mà \(x^2-5x+8=x^2-5x+\frac{25}{4}+\frac74=\left(x-\frac52\right)^2+\frac74>0\forall x\)

nên \(x^2-10x+8\le0\)

=>\(x^2-10x+25-17\le0\)

=>\(\left(x-5\right)^2\le17\)

=>\(-\sqrt{17}\le x-5\le\sqrt{17}\)

=>\(-\sqrt{17}+5\) <=x<=\(\sqrt{17}+5\)

ĐKXĐ: x∈R

\(\left(x+1\right)\left(2\sqrt{x^2+3}-x^2\right)+\sqrt[3]{3x^2+5}=5x+3\)

=>\(\left(x+1\right)\left(2\sqrt{x^2+3}-x^2\right)+\sqrt[3]{3x^2+5}-5x-3=0\)

=>\((x + 1)\left(2\sqrt{x^2 + 3} - x^2 - 3\right) + \left(\sqrt[3]{3x^2 + 5} - 2\right) - 2x + 2 = 0\)

\(\sqrt[3]{3x^2 + 5}-2\)

\(=\frac{3x^2 + 5 - 2^3}{\sqrt[3]{(3x^2+5)^2} + 2\sqrt[3]{3x^2+5} + 4}=\frac{3(x^2 - 1)}{\text{A}(x)}=\frac{3(x - 1)(x + 1)}{\text{A}(x)}\) , với A(x)=\(\sqrt[3]{(3x^2+5)^2}+2\sqrt[3]{3x^2+5}+4\)

\(2\sqrt{x^2 + 3}-(x^2+3)\)

\(=\frac{\left\lbrack2\sqrt{x^2 + 3}-(x^2+3)\right\rbrack\left\lbrack2\sqrt{x^2 + 3}+(x^2+3)\right\rbrack}{2\sqrt{x^2 + 3}+(x^2+3)}\)

=\(\frac{4(x^2 + 3) - (x^2 + 3)^2}{2\sqrt{x^2 + 3} + x^2 + 3}\quad\)

\(=\frac{\left(x^2+3\right)\left(4-x^2-3\right)}{2\sqrt{x^2+3}+\left(x^2+3\right)}=\frac{\left(x^2+3\right)\left(1-x\right)\left(1+x\right)}{2\sqrt{x^2+3}+\left(x^2+3\right)}\)

\((x+1)\left(2\sqrt{x^2 + 3}-x^2-3\right)+\left(\sqrt[3]{3x^2 + 5}-2\right)-2x+2=0\)

=>\(\left(x+1\right)\cdot\frac{\left(x^2+3\right)\left(1-x\right)\left(1+x\right)}{2\sqrt{x^2+3}+\left(x^2+3\right)}+\frac{3(x - 1)(x + 1)}{\text{A}(x)}-2\left(x-1\right)\) =0

=>(x-1)*G(x)=0

=>x-1=0

=>x=1(nhận)

a: ĐKXĐ: x>=1

\(\sqrt[3]{2-x}=1-\sqrt{x-1}\)

=>\(\sqrt[3]{2-x}-1+\sqrt{x-1}=0\)

=>\(\frac{2-x-1}{\sqrt[3]{\left(2-x\right)^2}+\sqrt[3]{2-x}+1}+\sqrt{x-1}=0\)

=>\(\frac{-\left(x-1\right)}{\sqrt[3]{\left(2-x\right)^2}+\sqrt[3]{2-x}+1}+\sqrt{x-1}=0\)

=>\(\sqrt{x-1}\left(-\frac{\sqrt{x-1}}{\sqrt[3]{\left(2-x\right)^2}+\sqrt[3]{2-x}+1}+1\right)=0\)

=>\(\sqrt{x-1}=0\)

=>x-1=0

=>x=1(nhận)