If x - 2y = 3 and xy = 5, find the value of x^2 - 4y^2.

We know that,

If x - y  = n

then, x + y  = \(\sqrt {n^2 + 4xy}\)

a² - b² = (a + b) (a – b)

Given data,

If x - 2y = 3

xy = 5,

then, x + 2y  = \(\sqrt {3^2 + 4(2×5)}\) = 7

find the value of $x^2 - 4y^2$ = ( x - 2y)( x + 2y)

= $x^2 - 4y^2$ = 3 × 7 = 21