Se (x+y)^2 - (x-y)^2 =48 então xy vale?
Soluções para a tarefa
Respondido por
6
( 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******
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******
Respondido por
5
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}} \\ \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}}](https://tex.z-dn.net/?f=%5C%5C+%5Cmathsf%7B%28x+%2B+y%29%5E2+-+%28x+-+y%29%5E2+%3D+48%7D+%5C%5C%5C%5C+%5Cmathsf%7B%5Cleft+%5B+%5Cmathsf%7B%28x+%2B+y%29+%2B+%28x+-+y%29%7D+%5Cright+%5D+%5Ccdot+%5Cleft+%5B+%5Cmathsf%7B%28x+%2B+y%29+-+%28x+-+y%29%7D+%5Cright+%5D+%3D+48%7D+%5C%5C%5C%5C+%5Cmathsf%7B%28x+%2B+y+%2B+x+-+y%29+%5Ccdot+%28x+%2B+y+-+x+%2B+y%29+%3D+48%7D+%5C%5C%5C%5C+%5Cmathsf%7B%282x%29+%5Ccdot+%282y%29+%3D+48%7D+%5C%5C%5C%5C+%5Cmathsf%7B4xy+%3D+48%7D+%5C%5C%5C%5C+%5Cboxed%7B%5Cmathsf%7Bxy+%3D+12%7D%7D)

Perguntas interessantes