acaho a,b,c là số nguyên thỏa mãn \(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}=\dfrac{1}{abc}\) .Chứng minh rằng :M=(1+a²)(1+b²)(1+c²) là số chính phương

Cho a,b,c thỏa mãn √a+√b-√c=√a+b-c.Chứng minh rằng \(\sqrt[2018]{a}+\sqrt[2018]{b}-\sqrt[2018]{c}=\sqrt[2018]{a+b-c}\)

Rút gọn :

a)\(A=\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+....+\dfrac{1}{\left(x+10\right)\left(x+11\right)}B=\dfrac{1}{x^2+x}+\dfrac{1}{x^2+3x+2}+\dfrac{1}{x^2+5x+6}+\dfrac{1}{x^2+7x+12}+\dfrac{1}{x^2+9x+20}\)

Rút gọn : \(\dfrac{a^3}{\left(a-b\right)\left(a-c\right)}+\dfrac{b^3}{\left(b-c\right)\left(b-a\right)}+\dfrac{c^3}{\left(c-a\right)\left(c-b\right)}\)

Tìm x,y ∈Z ,biết:

a)xy-2x+3y=8

b)2^x+7 =y²

c)4x²+4x+y²-6xy=15

d)x²-2xy+2y²+2y=8

e)x²-x-2=-y²

Tìm x,y ϵ Z⁺,biết :

(x+5)(y+6)=3xy