If a,b,c,d are in proportion, then prove that`(a^2+ab+b^2)/(a^2-ab+b^2)=(c^2+cd+d^2)/(c^2-cd+d^2)`

If a,b,c,d are in proportion, then prove that sqrt((a^2+5c^2)/(b^2+5d^2))=a/b

If a,b,c,d are in proportion, then prove that (11a^2+9ac)/(11b^2+9bd)=(a^2+3ac)/(b^2+3bd)

If a,b,c are in continued proportion, then prove that a/(a+2b)=(a-2b)/(a-4c)

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

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 =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 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^2+b^2)(b^2+c^2)=(ab+bc)^2

If x -iy = frac{a-ib}{c-id} , then prove that ( x^2 + y^2 ) = frac{a^2+b^2}{c^2+d^2}

If (a+ib)(c+id)(e+if)(g+ih) = A+ iB, then show that ( a^2 + b^2 ) ( c^2 + d^2 )( e^2 + f^2 )( g^2 + h^2 )= ( A^2 + B^2 )