\(Đkxđ:x\ge3+\sqrt{12}\) \(\sqrt{x^2+6x-3}=x-3\)
\(\Leftrightarrow\left(\sqrt{x^2+6x-3}\right)^2=\left(x-3\right)^2\)
\(\Leftrightarrow x^2+6x-3=x^2-6x+9\)
\(\Leftrightarrow x^2+6x-3-x^2+6x-9=0\)
\(\Leftrightarrow12x-12=0\)
\(\Leftrightarrow12x=12\)
\(\Leftrightarrow x=1\)
\(\sqrt{x^2-6x+11}\) +\(\sqrt{x^2-6x+13}+\sqrt{x^2-4x+5}=3+\sqrt{2}\)
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) \(x+\sqrt{17-x^2}+x\sqrt{17-x^2}=9\)
Rút gọn:
\(A=\frac{x^2+5x+6+x\sqrt{9-x^2}}{3x-x^2+\left(x+2\right).\sqrt{9-x^2}}\)
\(B=\frac{x^2-5x+6+3\sqrt{x^2-6x+8}}{3x-12+\left(x-3\right).\sqrt{x^2-6x+8}}\)
\(C=\frac{\sqrt{2\sqrt{4-x^2}}.\left(\sqrt{\left(2+x\right)^3}-\sqrt{\left(2-x\right)^3}\right)}{4+\sqrt{4-x^2}}\)
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:
a) \(x^2+6x-3=4x\sqrt{2x-1}\)
b) \(3x^2+4x-3=4x\sqrt{4x-3}\)
c) \(3x^2+2x+7=3\left(x+1\right)\sqrt{x^2+3}\)
d) \(6x^2+4x+8=5\left(x+1\right)\sqrt{2x^2+3}\)
e)\(6x^2-x=21+\left(x-3\right)\sqrt{x^2+x-6}\)
tìm x
a,\(\sqrt{3+\sqrt{x}}=4\)
b,\(\sqrt{x+3}=\sqrt{1-5x}\)
c,\(\sqrt{x^2+6x+9}=3x-1\)
Tính các giá trị của\(A=x^3-6x\) tại \(x=\sqrt[3]{14\sqrt{2}+20}+\sqrt[3]{-14\sqrt{2}+20}\)
Tìm x biết:
a)\(\sqrt{9x^2}=6\)
b)\(\sqrt{\left(x-2\right)^2}=5\)
c)\(\sqrt{x^2-6x+9}=3\)
d)\(\sqrt{x^2+4x+4}-2x=3\)
giải pt
a.\(2\sqrt{x-4}-\dfrac{1}{3}\sqrt{9x-36}=4-\sqrt{x-4}\)
b.\(3\sqrt{x-2}-\sqrt{x^2-4}=0\)
c.\(\sqrt{3x^2-18x+28}+\sqrt{4x^2-24x+45}=-5-x^2+6x\)
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) \(\left(x+1\right)\left(x+4\right)-3\sqrt{x^2+5x+2}=6\)