Ta có: \(\left(\sqrt{24-x^2}+\sqrt{8-x^2}\right)\left(\sqrt{24-x^2}-\sqrt{8-x^2}\right)=\left(\sqrt{24-x^2}^2-\sqrt{8-x^2}^2\right)\)

\(\Rightarrow\left(\sqrt{24-x^2}+\sqrt{8-x^2}\right)2=24-x^2-\left(8-x^2\right)\)

\(\Rightarrow2A=16\)

\(\Rightarrow A=8\)

Vậy \(A=8\).

1/\(\sqrt{24-x^2}-\sqrt{8-x^2}=2\)

\(\Rightarrow2A=\left(\sqrt{24-x^2}+\sqrt{8-x^2}\right)\left(\sqrt{24-x^2}-\sqrt{8-x^2}\right)\)

\(\Leftrightarrow2A=16\Rightarrow A=8\)

2/ ĐKXĐ : \(x\ge5\)

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

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

\(\Leftrightarrow2x+2\sqrt{x-2}.\sqrt{x-5}-7=x+3\)

\(\Rightarrow2\sqrt{x-2}.\sqrt{x-5}=10-x\)

\(\Leftrightarrow4\left(x-2\right)\left(x-5\right)=x^2-20x+100\)

\(\Leftrightarrow3x^2-8x-60=0\)

\(\Leftrightarrow\orbr{\begin{cases}x=6\\x=-\frac{10}{3}\end{cases}}\)

Vì \(x\ge5\) nên x = 6 thỏa mãn đề bài.

lớp 6 học căn đâu

\(\sqrt{24+8\sqrt{9-x^2}}=x+2\sqrt{3-x}+4\) \(\left(Đk:-3\le x\le3\right)\)

\(\sqrt{4\left(x+3\right)+8\sqrt{9-x^2}+4\left(3-x\right)}=x+2\sqrt{3-x}+4\)

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

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

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

\(4\left(x+3\right)=x^2+8x+14\)

\(x^2+4x+2=0\)

\(\Delta=16-8=8\)

\(\Delta>0\)=> phương trình có 2 nghiệm phân biệt

\(\left[{}\begin{matrix}x=\dfrac{-4+2\sqrt{2}}{2}=-2+\sqrt{2}\\x=\dfrac{-4-2\sqrt{2}}{2}=-2-\sqrt{2}\end{matrix}\right.\)