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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 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
Cau 1; cho\(\frac{x}{2}=\frac{y}{5}\)vaxy=90. So cap (x;y) thoa man la
Cau 2 : Cho a+d=b+c va \(a^2+d^2=b^2+c^2\)(b,d khac 0).Khi do 4 so lap thanh ti le thuc nao
Cau 3 :GTLN cua phan so \(\frac{7n-8}{2n-3}\)
Cau 4: Cho A=\(\frac{12}{x-15}\) dieu kien de 0<A<1 va A>1
Cau 5 ; tim x biet /-x-5//x=5=10
Cau 6: tap hop cac so nguyen cua x thoa man (3x^2-51)^2014=(-24)^2014
Cau 7: tap hop cac so thoa man /x-y/+/y+9/25/=0
chung minh rang neu a,b,c la cac so khac 0 thoa man
ab+ac/2=bc+ba/3=ca+cb/4 thi a/3=b/5=c/15
