Question

Se (x+y)^2 - (x-y)^2 =48 então xy vale?

Answer 1

( x + y )² - ( x - y )² = 48
xy = ?
( x² + 2.x.y + y²) - ( x² - 2.x.y + y² ) = 48
x² + 2xy + y² - ( x² - 2xy + y²) = 48
x² + 2xy + y² - x² + 2xy - y²  = 48
4xy = 48
xy = 48/4
xy = 12******

Answer 2

Outra...

$\\ \mathsf{(x + y)^2 - (x - y)^2 = 48} \\\\ \mathsf{\left [ \mathsf{(x + y) + (x - y)} \right ] \cdot \left [ \mathsf{(x + y) - (x - y)} \right ] = 48} \\\\ \mathsf{(x + y + x - y) \cdot (x + y - x + y) = 48} \\\\ \mathsf{(2x) \cdot (2y) = 48} \\\\ \mathsf{4xy = 48} \\\\ \boxed{\mathsf{xy = 12}}$



$\mathbf{Obs.: \ a^2 - b^2 = (a + b) \cdot (a - b)}$