Lời giải:
ĐKXĐ: $x\geq -2$
PT $\Leftrightarrow \frac{1}{5}\sqrt{25(x+2)}-5\sqrt{x+2}+\sqrt{9(x+2)}+9=0$
$\Leftrightarrow \sqrt{x+2}-5\sqrt{x+2}+3\sqrt{x+2}+9=0$
$\Leftrightarrow \sqrt{x+2}=9$
$\Rightarrow x=9^2-2=79$ (thỏa mãn)
Vậy.........
giải phương trình:
a/\(\frac{\sqrt{x}-2}{\sqrt{x}-5}=\frac{\sqrt{x}-4}{\sqrt{x}-6}\)
b/\(\sqrt{18x+9}-\sqrt{8x+4}+\frac{1}{3}\sqrt{2x+1}=4\)
c/\(\sqrt{4x-8}-\frac{1}{2}\sqrt{x-2}+\sqrt{9x-18}=9\)
Giải các phương trình sau:
a)\(\sqrt{3x+1}=\sqrt{4x-3}\)
b)\(\sqrt{9x+18}-5\sqrt{x+2}+\dfrac{4}{5}\sqrt{25x+50}=6\)
Rút gọn
a) \(A=\left(\frac{\sqrt{10}-\sqrt{5}}{\sqrt{8}-2}-\frac{\sqrt{90}}{3}\right).\frac{1}{\sqrt{5}}\)
b) \(B=\left(\frac{\sqrt{26}-\sqrt{13}}{1-\sqrt{2}}+\frac{\sqrt{18}-\sqrt{6}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{13}-\sqrt{6}}\)
c) \(C=\frac{\sqrt{10+2\sqrt{21}}-\sqrt{5-2\sqrt{6}}}{\sqrt{9-2\sqrt{14}}}\)
C=\(\sqrt{\left(\sqrt{5+2}\right)^2}-\sqrt{5}\)
D=\(\sqrt{8}+\sqrt{18}-\sqrt{32}\)
E=\(\sqrt{9-4\sqrt{5}}-\sqrt{5}\)
F=\(2\sqrt{8}-\sqrt{50}+\sqrt{\left(\sqrt{2}+1\right)^2}\)
B=\((\frac{x+3}{x-9}+\frac{1}{\sqrt{x}+3}):\frac{\sqrt{x}}{\sqrt{x}-3}\)) (vs x>0; x \(\ne\)9)
a,Rut gon B
b,Tinh gt cua B khi x=\(\sqrt{27+10\sqrt{2}}-\sqrt{18+8\sqrt{2}}\)
c,CM: B>\(\frac{1}{3}\)
(giup mk vs..)
Rút gọn biểu thức:
\(A=\frac{1}{\sqrt{1}-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-\frac{1}{\sqrt{4}-\sqrt{5}}\)
\(B=\left(\frac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\frac{4}{1+\sqrt{5}}+4\right)\)
\(C=\left(\frac{3+2\sqrt{3}}{\sqrt{3}+2}+\frac{2+\sqrt{2}}{\sqrt{2}+1}\right):\left(1:\frac{1}{\sqrt{2}+\sqrt{3}}\right)\)
\(D=2\sqrt{50}-\frac{1}{\sqrt{2}-1}+4\sqrt{\frac{9}{2}}-\sqrt{3-2\sqrt{2}}\)
\(\sqrt{\dfrac{x+2}{4}}+\sqrt{25x+50}-2\sqrt{x+2}=14\) ; \(\sqrt{2x+3}=x\) ; \(\sqrt{25x^2+20x+4}=1\) ; \(\sqrt{\dfrac{x+1}{2x-1}}=2\) ; \(\dfrac{\sqrt{x-2}}{\sqrt{3x+1}}=6\)
Tìm x
Giải phương trình :
\(\sqrt{8x-4}-\sqrt{\frac{25x}{2}-\frac{25}{4}}+2\sqrt{\frac{2x-1}{9}}=\frac{1}{2}\)
Bài 1. Tính:
a) \(\sqrt{\frac{5+\sqrt{21}}{5-\sqrt{21}}}+\sqrt{\frac{5-\sqrt{21}}{5+\sqrt{21}}}\) b) \(\left(2-\sqrt{2}\right)\sqrt{2+4\sqrt{3+\sqrt{2}+\sqrt{11-6\sqrt{2}}}}\)
c) \(\frac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-\sqrt{24}\right)}{\sqrt{75}-5\sqrt{2}}\) d) \(\frac{1}{\sqrt{25}+\sqrt{24}}+\frac{1}{\sqrt{24}+\sqrt{23}}+...+\frac{1}{\sqrt{2}+\sqrt{1}}\)
Bài 2. Tìm x
a) \(\sqrt{x-2\sqrt{x-1}}=2\) b) \(\sqrt{x^2-x}+\sqrt{x^2+x-2}=0\)
giúp tớ với, chiều nay tớ p ik hok rồi, thầy ktra bài tập nx
