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

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1.Relation and Function

hard

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

A

$xy$

B

${x^2} - {a^2}{y^2}$

C

$\frac{{{x^2} - {y^2}}}{4}$

D

$\frac{{{x^2} - {y^2}}}{{{a^2}}}$

Solution

(c) Given $f(x + ay,\,x – ay) = axy$…..$(i)$

Let $x + ay = u$ and $x – ay = v$

Then $x = \frac{{u + v}}{2}$ and $y = \frac{{u – v}}{{2a}}$

Substituting the value of $x$ and $y$ in $(i)$, we obtain

$f(u,v) = \frac{{{u^2} – {v^2}}}{4}$ ==> $f(x,\,y) = \frac{{{x^2} – {y^2}}}{4}$.

Standard 12

Mathematics

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