Carcass wrote:
If \(x^2+xy=100-y^2-xy\), what is the value of \((x \sqrt{3} + y \sqrt{3})^2\)?
Given: x² + xy = 100 - y² - xy
Add xy and y² to both sides of the equation to get:
x² + 2xy + y² = 100Now let's find the value of \((x \sqrt{3} + y \sqrt{3})^2\)
Use FOIL to expand and simplify: 3x² + 6xy + 3y²
Factor to get: 3(x² + 2xy + y²)
Substitute to get: 3(
100)
Evaluate: 300
Answer: 300