Question

If f(x + ay, x - ay) = axy then f(x,y) is equal to

• A. $\frac{x^2-y^2}{4}$
• B. $\frac{x^2+y^2}{4}$
• C. 4xy
• D. axy

Answer 1

The correct option is A $\frac{x^2-y^2}{4}$

$f(x+ay,x-ay)=axy$

Let $x+ay=m-i$ and $x-ay=n-i1$

Now, an adding (i) and(ii),

$$\begin{array}{c}2x=m+n\\ x=\frac{m+n}{2}\end{array}$$

and on subtraction (ii) from(i)

$$\begin{array}{c}2ay=m-n\\ y=\frac{m-n}{2a}\end{array}$$

Now, $\begin{array}{cc}f(m,n)& =a\times \frac{m+n}{2}\times \frac{m-n}{2a}\\ & =\frac{m^2-n^2}{4}\end{array}$

Replace $m$ by $x$ and $n$ by $y$

$f(x,y)=\frac{x^2-y^2}{4}$