ĐKXĐ: \(5\le x\le7\)
\(VT^2=x-5+7-x+2\sqrt{\left(x-5\right)\left(7-x\right)}=2+2\sqrt{\left(x-5\right)\left(7-x\right)}\le2+x-5+7-x=4\)
\(\Rightarrow VT\le2=VP\)
Dấu = xảy ra khi \(x-5=7-x\Leftrightarrow2x=12\Leftrightarrow x=6\)(thỏa mãn)
Giải phương trình
a,\(\sqrt{x-2+-\sqrt{2x-5}}+\sqrt{x+2+3\sqrt{2x+5}}=7\sqrt{2}\)
b,\(\sqrt{x+2-4\sqrt{x-2}}+\sqrt{x+7-6\sqrt{x}-2}=1\)
tìm x:
\(\sqrt{x^2+x+1}=1\)
\(\sqrt{x^2+1}=-3\)
\(\sqrt{x^2-10x+25}=7-2x\)
\(\sqrt{2x+5}=5\)
\(\sqrt{x^2-4x+4}-2x+5=0\)
tìm x
x-\(5\sqrt{x-2}=-2\)
\(\sqrt{x-2+\sqrt{2x-5}}+\sqrt{x+2+3\sqrt{2x-5}}=7\sqrt{2}\)
a. \(x+\sqrt{x}-2\)
b. \(x-9\)
c. \(x-3\sqrt{x}+2\)
d. \(x-5\sqrt{x}-6\)
e. \(x-4\)
f. \(x+7\sqrt{x}+12\)
g. \(x+\sqrt{x}\)
Bài 2
a) A= \(\sqrt{\left(1-\sqrt{2}\right)^2}+\sqrt{\left(-2\right)^6}-\sqrt{\left(1+\sqrt{2}\right)^2}\)
b) B= \(\sqrt{7+2\sqrt{6}}+\sqrt{7-2\sqrt{6}}\)
c) C= \(\sqrt{7-4\sqrt{3}}\)
d) D= \(2\sqrt{7+4\sqrt{3}}-\sqrt{13-4\sqrt{3}}\)
e) E= \(\frac{1}{1+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{5}}+...+\frac{1}{\sqrt{79}+\sqrt{81}}\)
Bài 4:
a) \(\sqrt{x-1}=2\)
b) \(\sqrt{x^2-3x+2}=\sqrt{2}\)
c) \(\sqrt{4x+1}=x+1\)
d) \(\sqrt{x+2\sqrt{x-1}}-\sqrt{x-2\sqrt{x-1}}=2\)
e) \(\sqrt{x^2-4x+5}+\sqrt{x^2-4x+8}+\sqrt{x^2-4x+9}=3+\sqrt{5}\)
f)
giải phương trình
\(\sqrt{x-2+\sqrt{2x-5}}+\sqrt{x-2-\sqrt{2x-5}}=7\sqrt{2}\)
Giải các phương trình sau:
\(2\sqrt{\left(x-2\right)\left(7-x\right)}-\sqrt{x-2}-\sqrt{7-x}=3\)
\(\dfrac{3x}{\sqrt{3x+10}}+1=\sqrt{3x+1}\)
\(\sqrt{7-x}+\sqrt{x-5}=x^2-12x+38\)
giải phương trình
1)\(\sqrt{31-x}=x-1\)
2)\(3\sqrt{x^2-1}=x^2+1\)
3)\(\sqrt{x^2-3x+5}+x=3x+7\)
Bài 1:
a) \(\sqrt{13-2\sqrt{42}}\)
b) \(\sqrt{46+6\sqrt{5}}\)
c) \(\sqrt{12-3\sqrt{15}}\)
d) \(\sqrt{11+\sqrt{96}}\)
Bài 2:
a) \(A=\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{4+2\sqrt{3}}}}\)
b) \(B=\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}\)
c) \(C=\sqrt{3-\sqrt{5}}\left(\sqrt{10}+\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
d) \(D=\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)
e) \(E=\sqrt{8+2\sqrt{10+2\sqrt{5}}}+\sqrt{8-2\sqrt{10+2\sqrt{5}}}\)
g) \(G=\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\)
h) \(H=4x-\sqrt{9x^2-12x+4}\)
i) \(\frac{\sqrt{7}-\sqrt{2}}{\sqrt{7}+\sqrt{2}}+\frac{\sqrt{7}+\sqrt{2}}{\sqrt{7}-\sqrt{2}}\)
Bài 1 :Tìm x để căn thức có nghĩa
a) \(\sqrt{-2\text{x}+3}\)
b)\(\sqrt{\frac{-5}{x^2+6}}\)
c)\(\sqrt{\frac{4}{x+3}}\)
Bài 2 : Rút gọn
a)\(\sqrt{\left(4+\sqrt{2}\right)^2}\)
b) 2\(\sqrt{3}\) + \(\sqrt{\left(2-\sqrt{3}\right)^2}\)
c) \(\sqrt{\left(3-\sqrt{3}\right)^2}\)
Bài 3
a) \(\sqrt{9-4\sqrt{5}}\) - \(\sqrt{5}\) = -2
b) \(\sqrt{23+8\sqrt{7}}\) - \(\sqrt{7}\) = 4
c) \(\left(4-\sqrt{7}\right)^2=23-8\sqrt{7}\)
Bài 4 : Rút gọn
a) \(\frac{x^2-5}{x+\sqrt{5}}\) với x khác \(\sqrt{5}\)
b) \(\frac{x^2+2\sqrt{2}+2}{x^2-2}\)
c) x - 4 +\(\sqrt{16-8\text{x}+x^2}\) với x >4
