For any a,b,x,y>0, prove that:

, where a=-ax by, β = bx + ay.

Given:-

Take

LHS

=

Dividing numerator and denominator of 1^{st} term and 2^{nd} term by b^{3} and y^{3} respectively.

=

=

We know that, Formula

Thus,

=

=

=

We know that, Formula

Thus,

=

=

=

As given,

ay + bx =β, -ax + by = α

=

We know that, Formula

Thus,

=

=

=

= RHS

So,

Hence Proved

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