cho a,b,c la 3 so thuc doi mot khac nhau va khac khong, thoa man: a+1/b=b+1/c=c+1/a. hay chung minh rang abc=1 hoac abc=-1

cho 3 so a,b,c khac thuoc Q khac nhau tung doi mot va khac 0 thoa man a/b+c=b/a+c=c/a+b

Chung minh b+c/a+a+c/b+a+b/c khong phu thuoc vao cac gia tri cua a,b,c

cho cac so a,b,c va thoa man \(\frac{ab}{a+b}=\frac{1}{3},\frac{bc}{b+c}=\frac{1}{4},\frac{ca}{c+a}=\frac{1}{5}\)Tinh gia tri bieu thuc P=\(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}\)

Cho ba so a , b, c thuoc Q khac nhau tung doi mot va khac 0 thoa man \(\dfrac{a}{b+c}=\dfrac{b}{a+c}=\dfrac{c}{a+b}\). Chung minh \(\dfrac{b+c}{a}+\dfrac{a+c}{b}+\dfrac{a+b}{c}\) khong phu thuoc vao cac so a , b, c

cho a, b, c, d la 4 so nguyen duong thoa man: b= \(\frac{a+c}{2}va\frac{1}{c}=\frac{1}{2}.\left(\frac{1}{b}+\frac{1}{d}\right)\)

chung minh: \(\frac{a}{b}=\frac{c}{d}\)

cho a,b,c khac 0 va thoa man 2ab+1/2b = 6bc+1/3c = 3ac+1/a chung minh a=2b=3c

cho a, b, c, d khac 0 va thoa man

ac=b^2; bd=c^2

chung minh \(\frac{a^3+b^3+c^3}{b^3+c^3+d^3}=\frac{a}{d}\)

cho cac so x,y,z khac 0 va thoa man \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=0\)      Chung minh rang  x²(y+z)+y²(z+x ) +z²(x+z)+3xyz

ai nnha nhat minh tik dung luon