Ta có:
\(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=\dfrac{1}{a+b+c}\)
\(\Leftrightarrow\left(a+b\right)\left(b+c\right)\left(c+a\right)=0\)
Tới đây thì đơn giản rồi nhé.
Cho a;b;c;x;y;z thỏa mãn
\(\dfrac{x^2+y^2+z^2}{a^2+b^2+c^2}=\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}+\dfrac{z^2}{c^2}\)
Tính gía trị \(\dfrac{x^{2017}+y^{2017}+z^{2017}}{2016}\)Hung nguyen
\(B=\dfrac{1}{\sqrt{x}+\sqrt{x+1}}+\dfrac{1}{\sqrt{x+1}+\sqrt{x+2}}+...+\dfrac{1}{\sqrt{x+2015}+\sqrt{x+2016}}\)với x = 2017
Bài 1: Tính
a, A= (1-\(\dfrac{1}{2}\))*(1-\(\dfrac{1}{3}\))*(1-\(\dfrac{1}{4}\))*...*(1-\(\dfrac{1}{2017}\))
b, B= \(\dfrac{1^2}{1\cdot2}\)*\(\dfrac{2^2}{2\cdot3}\)*\(\dfrac{3^2}{3\cdot4}\)*...*\(\dfrac{99^2}{99\cdot100}\)
Cho \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=\dfrac{1}{a+b+c}\)
Chứng minh rằng: \(\dfrac{1}{a^{2n+1}}+\dfrac{1}{b^{2n+1}}+\dfrac{1}{c^{2n+1}}=\dfrac{1}{a^{2n+1}+b^{2n+1}+c^{2n+1}}=\dfrac{1}{\left(a+b+c\right)^{2n+1}}\)
Tính M = \(\left(1-\dfrac{1}{2^2}\right)\left(1-\dfrac{1}{3^2}\right)\left(1-\dfrac{1}{4^2}\right)...\left(1-\dfrac{1}{2017^2}\right)\)
Cho a, b, c > 0. Chứng minh: \(\dfrac{2}{a+b}+\dfrac{2}{b+c}+\dfrac{2}{c+a}\le\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\)
Tìm max :
a) \(5-x^2\)
b) \(\dfrac{1}{5+x^2}\)
c) \(\dfrac{3}{x^2-4x+7}\)
d) \(-2x^2+3x+2017\)
\(Cho 3 số đôi một khác nhau. Chứng minh rằng : \(\dfrac{b-c}{\left(a-b\right)\left(a-c\right)}+\dfrac{c-a}{\left(b-c\right)\left(b-a\right)}+\dfrac{a-b}{\left(c-a\right)\left(c-b\right)}\) =\(2\left(\dfrac{1}{a-b}+\dfrac{1}{b-c}+\dfrac{1}{c-a}\right)\)\)
2) Tính giá trị biểu thức
a) P=(x+1) (x2-x+1)+x-(x-1) (x2+x+1)+2017 với x=-2017
b) Q=16x(4x2-5)-(4x+1) (16x2-4x+1) với x=\(\dfrac{1}{5}\)
