\(\sqrt{x^2-6x+9}=\sqrt{6+2\sqrt{5}}\)
\(\Leftrightarrow\left|x-3\right|=\sqrt{5}+1\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=\sqrt{5}+1\left(x\ge3\right)\\x-3=-\sqrt{5}-1\left(x< 3\right)\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4+\sqrt{5}\left(nhận\right)\\x=2-\sqrt{5}\left(nhận\right)\end{matrix}\right.\)
a)\(\sqrt{\sqrt{5}-\sqrt{3x}}\)
b) \(\sqrt{\sqrt{6x}-4x}\)
c) \(\sqrt{\left(\sqrt{x}-7\right)\left(\sqrt{x}+7\right)}\)
d) \(\sqrt{\left(x-6\right)^6}\)
e) \(\sqrt{-12x+5}\)
f) \(2-4\sqrt{5x+8}\)
g) \(\sqrt{x^2-9}\)
phương pháp 1 biến đổi về phương trình có chứa dấu giá trị tuyệt đối
1. \(\sqrt{x+3-4\sqrt{x-1}}+\sqrt{x+8+6\sqrt{x-1}}=5\)
2. \(\sqrt{x+2-3\sqrt{2x-5}}+\sqrt{x-2+\sqrt{2x-5}}=2\sqrt{2}\)
3. \(\sqrt{x+\sqrt{6x-9}}+\sqrt{x-\sqrt{6x-9}}=\sqrt{6}\)
4. \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=\dfrac{x+8}{5}\)
2.tìm x
a)\(\sqrt{x^2-6x+9}\)
b)\(\sqrt{x^2-2x+1}\)
c)\(\sqrt{4x+12}-3\sqrt{x+3}+7\sqrt{9x+27}=20\)
d)\(\sqrt{4x+20}+3\sqrt{\dfrac{x-5}{9}}-\dfrac{1}{3}\sqrt{9x-45}=6\)
\(\left(5\right)\sqrt{x+3-4\sqrt{x-1}}\sqrt{x+8+6\sqrt{x-1}}=5\)
\(\left(6\right)2x^2+3x+\sqrt{2x^2+3x+9}=33\)
\(\left(7\right)\sqrt{3x^2+6x+12}+\sqrt{5x^4-10x^2+30}=8\)
\(\left(8\right)x+y+z+8=2\sqrt{x-1}+4\sqrt{y-2}+6\sqrt{z-3}\)
Giải các phương trình
a,\(\sqrt{x^2-6x+9}=\sqrt{6-2\sqrt{5}}\)
b,\(\sqrt{9x^2-6x+1}-3\cdot\sqrt{\frac{7-4\sqrt{3}}{9}=0}\)
c,\(\sqrt{2x^2-4x+2}-\sqrt{3-\sqrt{5}}=0\)
a)\(\sqrt{9\left(2-3x\right)^2}=6\)
b)\(\sqrt{4x^2-9}=2\sqrt{2x+3}\)
c)\(\sqrt{10\left(x-3\right)}=\sqrt{20}\)
d)\(\sqrt{x^2+6x+9}=3x-6\)
A)\(\sqrt{x^2-4x+5}+\sqrt{x^2-4x+8}+\sqrt{x^2-4x+9}=3+\sqrt{5}\)
B)\(\sqrt{9x^2-6x+2}+\sqrt{45x^2-30x+9}=\sqrt{6x-9x^2+8}\)
GIẢI PHƯƠNG TRÌNH:
a)\(\sqrt{3x^2+6x+7}+\sqrt{5x^2+10x+14}=4-2x-x^2\)
b)\(\sqrt{x^2-4x+5}+\sqrt{x^2-4x+8}+\sqrt{x^2-4x+9}=3+\sqrt{5}\)
c)\(\sqrt{2-x^2+2x}+\sqrt{-x^2-6x-8}=1+\sqrt{3}\)
d)\(\sqrt{9x^2-6x+2}+\sqrt{45x^2-30x+9}=\sqrt{6x-9x^2+8}\)
Giải các phương trình dưới đây
1, \(\sqrt{9x^2-6x+2}+\sqrt{45x^2-30x+9}=\sqrt{6x-9x^2+8}\)
2,\(\sqrt{2x^2-4x+3}+\sqrt{3x^2-6x+7}=2-x^2+2x\)
3, \(\sqrt{6y-y^2-5}-\sqrt{x^2-6x+10}=1\) (x=3 ; y=3)
