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 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 gt 0 , then prove that (a+b)^2/(b+c)^2 = (a^2 +b^2)/(b^2 +c^2)

If b is the geometric mean of a and c, then show that a^2 b^2 c^2 [1/a^3 +1/b^3 +1/c^3] =a^3 +b^3 +c^3 .

If aY+z)=b(z+x)=c(x+y) and out of a,b,c no two of them are equal then show that, (y-z)/(a(b-c))=(z-x)/(b(c-a))(x-y)/(c(a-b))

If a,b,c,d are in G.P., then prove that: (b-c)^2 + (c-a)^2+(d-b)^2=(a-d)^2

If a,b,c re in continued proportion then show that a/c=(a^2+ab+b^2)/(b^2+bc+c^2)

If (y+z)/(a)=(z+x)/(b)=(x+y)/c then show that (x)/(b+c-a)=(y)/(c+a-b)=(z)/(a+b-c)

If (a+b+c)(a-b+c)=a^2+b^2+c^2 then show that a,b,c are in continued proportion.