" 10.If "2^(a)=3^(b)=6^(c)" then show that "c=(ab)/(a+b)

If 2^(a)=3^(b)=6^(c) then prove that c=(ab)/(a+b)

If a/b=b/c and a,b,c>0 then show that, (a^2+b^2)/(ab)=(a+c)/b

If a/b=b/c and a,b,c>0 then show that, (a+b+c)(b-c)=ab-c^2

If a/b=b/c and a,b,c>0 then show that, (a^2+b^2)(b^2+c^2)=(ab+bc)^2

If (5a-3b)/a= (4a+b-2c)/(a+4b-2c) = (a+2b-3c)/(4a-4c) , then show that 6a=4b=3c.

If a,b,c gt 0 show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)le(a+b+c)/2 .

IF a=2/3 , b=(-5)/6 and c=7/d ,show that (a-b)-c ne a-(b-c)

If c^(2) ne ab and the roots of (c^(2)-ab)x^(2)-2(a^(2)-bc)x+(b^(2)-ac)=0 are equal, then show that a^(3)+b^(3)+c^(3)=3abc" or "a=0

If a,b,c are in AP, show that (a(b+c))/(bc) , (b (c+a))/(ca), (c(a+b))/(ab) , are also in AP.

If a,b,c are unequal and positive then show that (bc)/(b+c)+(ca)/(c+a)+(ab)/(a+b)<1/2(a+b+c)