Ai giải giúp mấy bài toán vs
Bài 1:
A=\(\sqrt{\frac{1}{\text{√}2+1}-\frac{\text{√}8-\text{√}10}{2-\text{√}5}}\)
B=\(\frac{5\text{√}5}{\text{√}5+2}+\frac{\text{√}5}{\text{√}5-1}-\frac{3\text{√}5}{3+\text{√}5}\)
Bài 2 rút gọn biểu thức
A=\(\left(\frac{x+\sqrt[]{xy}}{\text{√}x+\text{√}y}-2\right):\frac{1}{\text{√}x+2}\) với x :y >0
B=\(\left(\frac{a}{a-2\text{√}a}+\frac{a}{\text{√}a-2}\right):\frac{\text{√}a+1}{a-4\text{√}a+4}\)
Bài 3 cho biểu thức
P=\(\left(\frac{x-2}{x+2\text{√}x}+\frac{1}{\text{√}x+2}\right)\frac{\text{√}x+1}{\text{√}x-1}\)
a)Rút gọn P
b)tìm x để P=\(\text{√}x+\frac{5}{2}\)
bài 4 rút gọn biểu thức
A=\(\frac{1}{x+\text{√}x}+\frac{2\text{√}x}{x-1}-\frac{1}{x-\text{√}x}\)
B=\(\left(\frac{x}{x+3\text{√}x}+\frac{1}{\text{√}x+3}\right):\left(1-\frac{2}{\text{√}x}+\frac{6}{x+3\text{√}x}\right)\)
Bài 5
A=\(\left(\frac{2}{\text{√}x-3}-\frac{1}{\text{√}x+3}-\frac{x}{\text{√}x\left(x-9\right)}\right):\text{(√}x+3-\frac{x}{\text{√}x-3}\)
a)rút gọn A
b)tìm gtri x để A= -1/4
AI GIẢI GIÙM MÌNH ĐI MÌNH TẠ ƠN
1. CHỨNG MINH ĐẲNG THỨC
a. \(\text{[}3+2\sqrt{6}-\sqrt{33}\text{]}\cdot\text{[}\sqrt{22}+\sqrt{6}+4\text{]}=24\)
b. \(\text{[}\frac{1}{5-2\sqrt{6}}+\frac{2}{5+2\sqrt{6}}\text{]}\cdot\text{[}15+2\sqrt{6}\text{]}\)
c.\(\text{[}\frac{4}{3}\cdot\sqrt{3}+\sqrt{2}+\sqrt{3\frac{1}{3}}\text{]}\cdot\text{[}\sqrt{1,2}+\sqrt{2}-4\sqrt{\frac{1}{5}}\text{]}=4\)
d. \(\sqrt{\text{[}1-\sqrt{1989}\text{]}^2}\cdot\sqrt{1990+2\sqrt{1989}}=1988\)
e. \(\frac{a-\sqrt{ab}+b}{a\sqrt{a}+b\sqrt{b}}-\frac{1}{a-b}=\frac{\sqrt{a}-\sqrt{b}-1}{a-b}\)với \(a>0;b>0\)và \(a\ne b\)
Bài 1 Rút gọn và tính
a, \(\sqrt{\frac{\sqrt{a}-1}{\sqrt{b}+1}}:\sqrt{\frac{\sqrt{b}-1}{\sqrt{a}+1}}\)với a=7.25;b=3.25
b,\(\sqrt{15\text{a}^2-8\text{a}\sqrt{15}+16}\) với \(a=\sqrt{\frac{3}{5}}+\sqrt{\frac{5}{3}}\)
c,\(\sqrt{10\text{a}^2-4\text{a}\sqrt{10}+4}\)với \(a=\sqrt{\frac{2}{5}}+\sqrt{\frac{5}{2}}\)
d,\(\sqrt{a^2+2\text{a}\sqrt{a^2-1}}-\sqrt{a^2-2\sqrt{a^2-1}}v\text{ới}\)\(a=\sqrt{5}\)
tính: \(\text{[}\sqrt{2}-1\text{]}^2-\frac{3}{2}\cdot\sqrt{\text{[}-2\text{]}^2}+\frac{4\sqrt{2}}{5}+\sqrt{1\frac{11}{25}}\cdot\sqrt{2}\)
Chứng minh: \(\sqrt{x}\cdot\text{[}1-\sqrt{x}\text{]}\le\frac{1}{4}v\text{ới}x\ge0\)
Tính giá trị biểu thức:
\(\text{a) }\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+...+\frac{1}{\sqrt{2010}+\sqrt{2011}}\)
\(\text{b) }\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{121\sqrt{120}+120\sqrt{121}}\)
\(\text{c) }\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+...\sqrt{+1+\frac{1}{2010^2}+\frac{1}{2011^2}}\)
Bài 1: cho P= \(\left(\frac{\sqrt{b}}{\sqrt{a}-\sqrt{a-b}}\text{+}\frac{\sqrt{b}}{\sqrt{a}\text{+}\sqrt{a\text{+}b}}\right)\div\left(1\text{+}\frac{\sqrt{a\text{+}b}}{\sqrt{a-b}}\right)\)
a) Rút gọn P
b) Tính P khi a=\(24-2\sqrt{15}\); b=16
Bài 2: \(x\ge0\), cm: \(x^2-3\sqrt{x}\text{+}\frac{5}{2}\)>0
Đề: Cho biểu thức
A=\(\frac{\text{15√x−11}}{x+2\sqrt{x}−3}-\frac{\text{3√x−2}}{1−\sqrt{x}}-\frac{3}{\text{√x+3}}\text{(x≥0;x≠1) }\)
a. Thu gọn biểu thức A
b. Tìm x nguyên để A nguyên
\(\text{Tính }C=\frac{\left(1+\sqrt{3}\right)x^2y-\left(2-\sqrt{5}\right)xy^2}{x^3+y^3}\text{ với }x,y\ne0\text{ và }\frac{x}{4}=\frac{y}{7}\)
\(T\text{ìm}\) \(s\text{ố}.nguy\text{ê}n.d\text{ư}\text{ơ}ng.nh\text{ỏ}.nh\text{ất}.th\text{ỏa}.m\text{ãn}:\frac{1}{2}s\text{ố}.\text{đ}\text{ó}.l\text{à}.s\text{ố}.ch\text{ính}.ph\text{ư}\text{ơ}ng\) \(\frac{1}{3}s\text{ố}.\text{đ}\text{ó}.l\text{à}.l\text{ập}.ph\text{ư}\text{ơ}ng.c\text{ủa}.1.s\text{ố}.nguy\text{ên}\) \(\)
\(\frac{1}{5}s\text{ố}.\text{đ}\text{ó}.l\text{à}.l\text{ũy}.th\text{ừa}.5.c\text{ủa}.1.s\text{ố.nguy\text{ê}n}\)