If ` a : b = x : y `, then show that ` (a^(2) + b^(2)) : a^(3)/(a + b) : : (x^(2) + y^(2)) : x^(3)/(x + y) `

If a/b = x/y , then show that (a+b) (a^(2)+b^(2))x^(3) = (x+y)(x^(2)+y^(2))a^(3)

If a(y+z)=b(z+x)=c(x+y) then show that (a-b)/(x^(2)-y^(2))=(b-c)/(y^(2)-z^(2))=(c-a)/(z^(2)-x^(2))]

If a = x+y, b=x-y and c = x+2y , then show that a^3+b^3+c^3-3abc =7y^2(3x+2y)

If y^2 = a^2 cos^2 x + b^2 sin^2 x, show that y + (d^2 y)/(dx^2) = (a^2 b^2)/ (y^3)

If x= a cos theta , y= b sin theta , show that ( d^2 y)/(d x^2 ) = - b^4 /a^2y^3

{:("Column" A ,, "Column" B), ((3x^(2) - 5)- (2x^(2) - 5 + y^(2)) ,, (a) x^(2) + xy + y^(2)) , (9x^(2) - 16y^(2) ,, (b) 2) , ((x^(3) - y^(3))/(x-y) ,, (c) (9x + 16y) (9x - 16y)) , ("The degree of " (x + 2) (x+3) ,, (d) x^(2) - y^(2)) , (,, (e) 1) , (,, (f) (3x + 4y) (3x - 4y)):}

If (a+b)x =a and (a+b) y = b then the value of (x^(2)+y^(2))/(x^(2)-y^(2)) is

If (x+y)/(3a-b) = (y+z)/(3b-c) = (z+x)/(3c-a) , then show that (x+y+z)/(a+b+c)= (ax + by+cz)/(a^(2)+b^(2)+c^(2))