1: \(=3+2\sqrt{2}+\sqrt{5}-2=2\sqrt{2}+\sqrt{5}+1\)
2: \(=3+2\sqrt{2}-3+2\sqrt{2}=4\sqrt{2}\)
3: \(=\dfrac{\sqrt{7}-\sqrt{5}}{2}-\dfrac{2\left(\sqrt{7}+1\right)}{6}\)
\(=\dfrac{3\sqrt{7}-3\sqrt{5}-2\sqrt{7}-2}{6}=\dfrac{\sqrt{7}-3\sqrt{5}-2}{6}\)
\(a.\dfrac{4}{\text{√ }3+1}-\dfrac{5}{\text{√ }3-2}+\dfrac{6}{3-\text{√ }3}\)
b.√ 2x - √ 8x+\(\dfrac{1}{2}\text{√ }2x=2\)
Cho abc=1
CM: \(\dfrac{\text{1}}{\text{a}^2+2b^2+3}=\dfrac{\text{1}}{b^2+2c^2+3}=\dfrac{\text{1}}{c^2+2a^2+3}\) ≤ \(\dfrac{\text{1}}{\text{2}}\)
1 a..Rút gọn biểu thức A = \(\dfrac{\text{ x 2 − 4 x + 4}}{\text{x 3 − 2 x 2 − ( 4 x − 8 ) }}\)
b. Rút gọn biểu thức B = \(\left(\dfrac{x+2}{\text{x }\sqrt{\text{x }}+1}-\dfrac{1}{\sqrt{\text{x}}+1}\right).\dfrac{\text{4 }\sqrt{x}}{3}\)
1. Tìm max và min
a) \(A=\sqrt{x-3}+\sqrt{7-x}\)
b) \(B=\dfrac{3+8x^2+12x^4}{\left(1+2x^2\right)^2}\)
2. Cho \(36x^2+16y^2=9\)
\(CM:\dfrac{15}{4}\text{≤}y-2x+5\text{≤}\dfrac{25}{4}\)
1. Rút gọn biểu thức A = \(\dfrac{\text{√ x + 1}}{\text{√ x − 1 }}-\dfrac{\text{√ x − 1}}{\text{√ x + 1}}+\dfrac{\text{8 √ x}}{\text{1 − x }}\)
2. Rút gọn biểu thức B = \(\dfrac{\text{√ x − x − 3}}{\text{x − 1 }}-\dfrac{\text{1}}{\text{√ x − 1 }}\) với x ≥ 0, x ≠ 1
\(\left(\dfrac{\text{√}x}{\text{√}x+2}+\dfrac{8\text{√}x+8}{x+2\text{√}x}-\dfrac{\text{√}x+2}{\text{√}x}\right):\left(\dfrac{x+\sqrt{x}+3}{x+2\sqrt{x}}+\dfrac{1}{\sqrt{x}}\right)\)
a) rút gọn P
b)CMR: P≤1
Tìm x,
a, \(\dfrac{\text{√(2x-3)}}{\text{√(x-1)}}=2\)
b, \(\text{ }\sqrt{\dfrac{2x-3}{x-1}}=2\)
Rút gọn biểu thức C = \(\dfrac{\text{x}-\dfrac{\text{1}}{\text{x}^{\text{2}}}}{\text{1}+\dfrac{1}{x}+\dfrac{1}{x^2}}\)
Cho abc=1. Tìm max
\(\text{M}=\dfrac{\text{1}}{\text{2ab+ca+3}}+\dfrac{\text{1}}{\text{2ca+bc+3}}+\dfrac{\text{1}}{\text{2bc+ab+3}}\)
Bài 1 :
a) Cho 3 số hữu tỉ a,b,c thoả mãn : \(\dfrac{1}{a}+\dfrac{1}{b}\text{=}\dfrac{1}{c}\). Chứng minh rằng : \(A\text{=}\sqrt{a^2+b^2+c^2}\) là số hữu tỉ.
b) Cho 3 số x,y,z đôi một khác nhau . Chứng minh rằng : \(B\text{=}\sqrt{\dfrac{1}{\left(x-y\right)^2}+\dfrac{1}{\left(y-z\right)^2}+\dfrac{1}{\left(z-x\right)^2}}\) là một số hữu tỉ.
