Cho a,b,c thỏa mãn a+b+c = 2021 và \(\dfrac{1}{a+b}+\dfrac{1}{b+c}+\dfrac{1}{c+a}=\dfrac{1}{2021}\)

Tính Q = \(\dfrac{a}{b+c}+\dfrac{b}{c+a}+\dfrac{c}{a+b}\)

Tìm a,b,c biết \(\dfrac{3c-4b}{2}=\dfrac{4a-2c}{3}=\dfrac{2b-3a}{4}\) và c+b-a = -30

Cho a,b,c thỏa mãn: \(\dfrac{a+b}{3}=\dfrac{b+c}{4}=\dfrac{c+a}{5}\) 

Tính M = 10a+b-7c+2021

Tính B = \(\left(1-\dfrac{1}{3}\right)\left(1-\dfrac{1}{6}\right)\left(1-\dfrac{1}{10}\right)\left(1-\dfrac{1}{15}\right)...\left(1-\dfrac{1}{2450}\right)\)

Cho a+b+c+d ≠ 0 thỏa mãn: 
\(\dfrac{a}{b+c+d}=\dfrac{b}{a+c+d}=\dfrac{c}{b+a+d}=\dfrac{d}{c+b+a}\)

Tính P = \(\dfrac{2a+5b}{3c+4d}+\dfrac{2b+5c}{3d+4a}+\dfrac{2c+5d}{3a+4b}+\dfrac{2d+5a}{3c+4b}\)

Cho x,y,z thỏa mãn: \(\dfrac{3x-2y+z}{x}\) = \(\dfrac{3y-2z+x}{y}\) = \(\dfrac{3z-2x+y}{z}\)

Tính Q = \(\dfrac{x+y}{z}+\dfrac{y+z}{x}+\dfrac{z+x}{y}\)

Cho x,y,z ≠ 0 thỏa mãn: 2(x+y) = 3(y+z) = 4(x+z)
Tính P = \(\dfrac{x}{y}\)+\(\dfrac{y}{z}\)+\(\dfrac{z}{x}\)

Tìm x,y nguyên biết 
a/ |x - 3| + |2y - 6| + 10 = \(\dfrac{30}{\left(y-3\right)^2+3}\)

b/ (2x + 6)²⁰²⁰ + 51 = \(\dfrac{102}{3\left|x+3\right|+2}\)

a/ Cho M=\(\dfrac{\sqrt{x}-1}{2}\). Tìm x ∈ Z để M ∈ Z biết x<50

b/ Cho N=\(\dfrac{9}{\sqrt{x}-5}\). Tìm x ∈ Z để N ∈ Z