a: ĐKXĐ: x>=-4

\(x^2+3x+24=12\sqrt{x+4}\)

=>\(x\left(x+3\right)-12\sqrt{x+4}+24=0\)

=>\(x\left(x+3\right)-12\left(\sqrt{x+4}-2\right)=0\)

=>\(x\left(x+3\right)-12\cdot\frac{x+4-4}{\sqrt{x+4}+2}=0\)

=>\(x\left(x+3\right)-\frac{12x}{\sqrt{x+4}+2}=0\)

=>\(x\left(x+3-\frac{12}{\sqrt{x+4}+2}\right)=0\)

=>\(x\left\lbrack x+\frac{3\sqrt{x+4}+6-12}{\sqrt{x+4}+2}\right\rbrack=0\)

=>\(x\left\lbrack x+\frac{3\sqrt{x+4}-6}{\sqrt{x+4}+2}\right\rbrack=0\)

=>\(x\cdot\left\lbrack x+\frac{3\left(\sqrt{x+4}-2\right)}{\sqrt{x+4}+2}\right\rbrack=0\)

=>\(x\cdot\left\lbrack x+3\cdot\frac{x+4-4}{\left(\sqrt{x+4}+2\right)\left(\sqrt{x+4}+2\right)}\right\rbrack=0\)

=>\(x^2\left(1+\frac{3}{\left(\sqrt{x+4}+2\right)^2}\right)=0\)

=>\(x^2=0\)

=>x=0(nhận)

b:

ĐKXĐ: x>=-5/2

\(x^2+\sqrt{2x+5}=2x+3+\sqrt{x^2+2}\)

=>\(x^2-2x-3=\sqrt{x^2+2}-\sqrt{2x+5}\)

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

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

=>(x-3)(x+1)=0

=>\(\left[\begin{array}{l}x=3\left(nhận\right)\\ x=-1\left(nhận\right)\end{array}\right.\)

ĐKXĐ: x>0

Ta có: \(\frac{\sqrt{x}-1}{x-\sqrt{x}+1}-\frac{1}{\sqrt{x}+1}\)

\(=\frac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)-\left(x-\sqrt{x}+1\right)}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}\)

\(=\frac{x-1-x+\sqrt{x}-1}{\left(\sqrt{x}+1\right)\left(x-\sqrt{x}+1\right)}=\frac{\sqrt{x}-2}{\left(\sqrt{x}+1\right)\cdot\left(x-\sqrt{x}+1\right)}\)

Ta có: \(A=\left(x+\frac{1}{\sqrt{x}}\right)\left(\frac{\sqrt{x}-1}{x+\sqrt{x}+1}-\frac{1}{\sqrt{x}+1}\right)\)

\(=\frac{x\sqrt{x}+1}{\sqrt{x}}\cdot\frac{\sqrt{x}-2}{x\sqrt{x}+1}=\frac{\sqrt{x}-2}{\sqrt{x}}\)

Để A nguyên thì \(\sqrt{x}-2\) ⋮\(\sqrt{x}\)

=>-2⋮\(\sqrt{x}\)

=>\(\sqrt{x}\) ∈{1;2}

=>x∈{1;4}

\(a=\sqrt[3]{7+5\sqrt2}+\sqrt[3]{7-5\sqrt2}\)

\(=\sqrt[3]{2\sqrt2+6+\sqrt2+1}+\sqrt[3]{2\sqrt2-6+\sqrt2-1}\)

\(=\sqrt[3]{\left(\sqrt2\right)^3+3\cdot\left(\sqrt2\right)^2\cdot1+3\cdot\sqrt2\cdot1^2+1^3}+\sqrt[3]{\left(\sqrt2\right)^3-3\cdot\left(\sqrt2\right)^2\cdot1+3\cdot\sqrt2\cdot1^2-1^3}\)

\(=\sqrt[3]{\left(\sqrt2+1\right)^3}+\sqrt[3]{\left(\sqrt2-1\right)^3}=\sqrt2+1+\sqrt2-1=2\sqrt2\)

\(D=2a^4+6a^2-28a+2024\)

\(=2\cdot\left(2\sqrt2\right)^4+6\cdot\left(2\sqrt2\right)^2-28\cdot2\sqrt2+2024=2200-56\sqrt2\)

giải hộ mik bài 4 ạ

thân ai nấy lo đi nhé

b) \(\sqrt{x^2}=\left|-8\right|\)

\(\Rightarrow\left|x\right|=8\)

\(\Rightarrow\left[{}\begin{matrix}x=8\\x=-8\end{matrix}\right.\)

d) \(\sqrt{9x^2}=\left|-12\right|\)

\(\Rightarrow\sqrt{\left(3x\right)^2}=12\)

\(\Rightarrow\left|3x\right|=12\)

\(\Rightarrow\left[{}\begin{matrix}3x=12\\3x=-12\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{12}{3}\\x=-\dfrac{12}{3}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)

ĐKXĐ: \(\left\{{}\begin{matrix}2x-3>=0\\x+1>=0\end{matrix}\right.\)

=>\(\left\{{}\begin{matrix}x>=\dfrac{3}{2}\\x>=-1\end{matrix}\right.\)

=>\(x>=\dfrac{3}{2}\)

\(\sqrt{2x-3}-\sqrt{x+1}=x-4\)

=>\(\dfrac{2x-3-x-1}{\sqrt{2x-3}+\sqrt{x+1}}-\left(x-4\right)=0\)

=>\(\left(x-4\right)\left(\dfrac{1}{\sqrt{2x-3}+\sqrt{x+1}}-1\right)=0\)

=>x-4=0

=>x=4(nhận)