If f(x + 2y, x - 2y) = xy, then f(x, y) is equal to

Question

If f(x + 2y, x - 2y) = xy, then f(x, y) is equal to (A) (1/4)xy (B) (1/4)(x2-y2) (C) (1/8)(x2-y2) (D) (1/2)(x2+y2)

Tardigrade Admin · Accepted Answer

Given f(x+2 y, x-2 y)=x y...(i) Let a=x+2 y and b=x-2 y ∴ a+b=2 x and a-b=4 y From Eq. (i), we get f(a, b) =((a+b/2))((a-b/4)) =(a2-b2/8) ∴ f(x, y) =(x2-y2/8)

Q. If $f (x + 2 y, x - 2 y) = x y$ , then $f (x, y)$ is equal to

$\frac{1}{4} x y$

$\frac{1}{4} (x^{2} - y^{2})$

$\frac{1}{8} (x^{2} - y^{2})$

$\frac{1}{2} (x^{2} + y^{2})$

Given $f (x + 2 y, x - 2 y) = x y$ ...(i)
Let $a = x + 2 y$ and $b = x - 2 y$
$∴ a + b = 2 x$ and $a - b = 4 y$
From Eq. (i), we get
$f (a, b) = (\frac{a + b}{2}) (\frac{a - b}{4})$
$= \frac{a ^{2} - b ^{2}}{8}$
$∴ f (x, y) = \frac{x ^{2} - y ^{2}}{8}$

Q. If f(x+2y,x−2y)=xy, then f(x,y) is equal to

41​xy

41​(x2−y2)

81​(x2−y2)

21​(x2+y2)