ĐKXĐ: \(-1\le x\le7\)
Ta có: \(VT\le\sqrt{2\left(x+1+7-x\right)}=4\)
\(VP=\left(x-3\right)^2+4\ge4\)
\(\Rightarrow VT\le VP\)
\(\Rightarrow\) BPT có nghiệm khi \(VT=VP\Leftrightarrow\left\{{}\begin{matrix}x+1=7-x\\x-3=0\end{matrix}\right.\) \(\Rightarrow x=3\)
\(\sqrt{7-x}+\sqrt{x+1}=\sqrt{x^2-6x+13}\)
Giải các phương trình sau:
a) \(\sqrt{x^2-6x+9}=4-x\)
b) \(\sqrt{2x-2+2\sqrt{2x-3}}+\sqrt{2x+13+8\sqrt{2x-3}}=5\)
giải pt:
a) x+2\(\sqrt{7-x}\) = \(2\sqrt{x-1}+\sqrt{-x^2+8x-7+1}\)
b) \(2x^2-6x+4=\sqrt[3]{x^3+8}\)
c) \(2.\sqrt[3]{3x-2}+\sqrt[3]{6x-5}=8\)
d) \(x+\sqrt{17-x^2}+x\sqrt{17-x^2}=9\)
giải các phương trình
1) \(\sqrt{4x-20}\) +3\(\sqrt{\dfrac{x-5}{9}}\) \(-\dfrac{1}{3}\sqrt{9x-45}=6\)
2)\(\sqrt{x+1}+\sqrt{x+6}=5\)
3) \(x^2-6x+\sqrt{x^2-6x+7}=5\)
4)\(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=4\)
5)\(\sqrt{x^2-\dfrac{1}{4}+\sqrt{x^2+x+\dfrac{1}{4}}}=\dfrac{1}{2}\left(2x^3+x^2+2x+1\right)\)
6)\(\sqrt{3x^2+6x+12}+\sqrt{5x^4-10x^2+30}=8\)
7)\(\sqrt{3x^2+6x+7}+\sqrt{5x^2+10x+14}=4-2x-x^2\)
Giải các phương trình sau:
a)x2-6x+\(\sqrt{x^2-6x+7}\)=5
b)\(\sqrt{x+1}+\sqrt{x+6}=5\)
c)\(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8-6\sqrt{x-1}}=4\)
Giải giúp mình nhé cảm ơn mọi người ^^
Giải phương trình sau:
a) \(\sqrt{4x+20}-3\sqrt{5+x}+\dfrac{4}{3}\sqrt{9x+45}=6\)
b) \(\dfrac{1}{2}\sqrt{x-1}-\dfrac{3}{2}\sqrt{9x-9}+24\sqrt{\dfrac{x-1}{64}}=-17\)
c) \(2x-x^2+\sqrt{6x^2-12x+7}=0\)
d) \(\left(x+1\right)\left(x+4\right)-3\sqrt{x^2+5x+2}=6\)
Rút gọn
a, \(\sqrt{4+\sqrt{7+4\sqrt{3}}}\)
b, \(\sqrt{5+\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
c, \(\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
d, \(\sqrt{x+2\sqrt{x}-1}\)+ \(\sqrt{x-2\sqrt{x-1}}\) ( x \(\ge\)0)
Rút gọn
\(A=\frac{\sqrt{x}}{\sqrt{x}-2}+\frac{\sqrt{x}-1}{\sqrt{x}+2}+\frac{\sqrt{x}-10}{x-4}\) (x\(\ge\)0, x \(\ne\) 4)
\(B=\left(13-4\sqrt{3}\right)\left(7+4\sqrt{3}\right)-8\sqrt{20+2\sqrt{43+24\sqrt{3}}}\)
giúp giải ptr vs
a.\(\sqrt{4x+1}-\sqrt{3x+4}=\sqrt{x-2}\)
b.\(\sqrt{x-2}-\sqrt{x+1}=\sqrt{2x-1}-\sqrt{x+3}\)
c.\(\sqrt{4x+1}-\sqrt{7+x}=2\sqrt{2x-3}+\sqrt{5-6x}\)
