1.If `x/a` =` y/b` , a+b `!=` 0 show that `(x^2 + a^2 )/( x+a)` + `(y^2 + b^2 )/( y+b)` =` ((x+y)^2 + (a+b)^2)/((x+y) + (a+b))`

If (a^(2) + b^(2)) (x^(2) + y^(2)) = (ax + by)^(2) , prove that : (a)/(x) = (b)/(y) .

x/a-y/b=0 , a x+b y=a^2+b^2

Show that |a b c a+2x b+2y c+2z x y z|=0

The foci of hyperbola xy = ((a^2 + b^2)/(4)) are given by (A) x = y = +- ((a^2 + b^2)/(4a)) (B) x = y = +- ((a^2 + b^2)/(4b)) (C) x = y = +- ((a^2 + b^2)/(2a)) (D) x = y = +- ((a^2 + b^2)/(2b))

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

Prove that (a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot

Prove that (a b+x y)(a x+b y)>4a b x y(a , b ,x ,y >0)dot

Solve for 'x' and 'y': (a -b) x + (a + b) y =a^2 - b^2 - 2ab and (a + b) (x + y) = a ^2+ b^2

Prove that: |a b a x+b y b c b x+c y a x+b y b x+c y0|=(b^2-a c)(a x^2+2b x y+c y^2) .

Solve (x)/(a) + (y)/(b) = 1 and a(x - a)- b(y + b) = 2a^(2) + b^(2) .