e/ ĐKXĐ: \(-1\le x\le4\)
Tưởng nó giống câu c mà ko phải
\(\Leftrightarrow\sqrt{x+1}+\sqrt{4-x}+\sqrt{\left(4-x\right)\left(x+1\right)}=5\)
Đặt \(\sqrt{x+1}+\sqrt{4-x}=a>0\Rightarrow a^2=5+2\sqrt{\left(x+1\right)\left(4-x\right)}\)
\(\Rightarrow\sqrt{\left(x+1\right)\left(4-x\right)}=\frac{a^2-5}{2}\) pt trở thành:
\(a+\frac{a^2-5}{2}=5\Leftrightarrow a^2+2a-15=0\Rightarrow\left[{}\begin{matrix}a=3\\a=-5\left(l\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{x+1}+\sqrt{4-x}=3\)
\(\Leftrightarrow5+2\sqrt{-x^2+3x+4}=9\)
\(\Leftrightarrow\sqrt{-x^2+3x+4}=2\)
\(\Leftrightarrow-x^2+3x=0\Rightarrow\left[{}\begin{matrix}x=0\\x=3\end{matrix}\right.\)
b/ĐKXĐ: \(0\le x\le4\)
\(\Leftrightarrow\left(3x-7\right)\sqrt{x\left(4-x\right)}+4-x=0\)
\(\Leftrightarrow\sqrt{4-x}\left[\left(3x-7\right)\sqrt{x}+\sqrt{4-x}\right]=0\)
\(\Rightarrow\left[{}\begin{matrix}x=4\\\sqrt{4-x}=\left(7-3x\right)\sqrt{x}\left(x\le\frac{7}{3}\right)\end{matrix}\right.\)
\(\Leftrightarrow4-x=x\left(7-3x\right)^2\)
\(\Leftrightarrow4-x=x\left(9x^2-42x+49\right)\)
\(\Leftrightarrow9x^3-42x^2+50x-4=0\)
\(\Leftrightarrow\left(x-2\right)\left(9x^2-24x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=\frac{4+\sqrt{14}}{3}>\frac{7}{3}\left(l\right)\\x=\frac{4-\sqrt{14}}{3}\end{matrix}\right.\)
a/ Bạn kiểm tra lại, đề là \(2\sqrt{x-x^3}\) hay \(2\sqrt{x-x^2}\)
b/ Như trên, trong căn là bậc 2 hay bậc 3? Bậc 3 thì hầu như không thể giải
c/ ĐKXĐ: \(-1\le x\le1\)
\(\Leftrightarrow\sqrt{1-x}+\sqrt{4-x}+\sqrt{\left(4-x\right)\left(x+1\right)}=5\)
\(\Leftrightarrow1-\sqrt{1-x}+2-\sqrt{4-x}+2-\sqrt{4+3x-x^2}=0\)
\(\Leftrightarrow\frac{x}{1+\sqrt{1-x}}+\frac{x}{2+\sqrt{4-x}}+\frac{x\left(x-3\right)}{2+\sqrt{4+3x-x^2}}=0\)
\(\Leftrightarrow x\left(\frac{1}{1+\sqrt{1-x}}+\frac{1}{2+\sqrt{4-x}}+\frac{x-3}{2+\sqrt{4+3x-x^2}}\right)=0\)
\(\Rightarrow x=0\)
d/ ĐKXĐ: \(-3\le x\le6\)
\(\Leftrightarrow\sqrt{3+x}+\sqrt{6-x}-\sqrt{18+3x-x^2}-3=0\)
Đặt \(\sqrt{3+x}+\sqrt{6-x}=a>0\Rightarrow a^2=9+2\sqrt{18+3x-x^2}\)
\(\Rightarrow\sqrt{18+3x-x^2}=\frac{a^2-9}{2}\) pt trở thành:
\(a-\frac{a^2-9}{2}-3=0\Leftrightarrow-a^2+2a+3=0\Rightarrow\left[{}\begin{matrix}a=-1\left(l\right)\\a=3\end{matrix}\right.\)
\(\Rightarrow\sqrt{3+x}+\sqrt{6-x}=3\)
\(\Leftrightarrow9+2\sqrt{\left(3+x\right)\left(6-x\right)}=9\)
\(\Leftrightarrow\sqrt{\left(x+3\right)\left(6-x\right)}=0\Rightarrow\left[{}\begin{matrix}x=-3\\x=6\end{matrix}\right.\)
Sửa câu b) \(x+\sqrt{4x-x^2}=4+3\left(x-2\right)\sqrt{4x-x^2}\)
Nguyễn Việt Lâm giúp mk nhesssss, thekiu :>
