Largest Possible Value

Algebra Level 2

It is given that $-2 \leq x \leq 4$ and $-4\leq y \leq 1$ , find the largest possible value of $(x+y)(x-y)$ .

1 solution

Akshat Sharda
Mar 2, 2016

$(x+y)(x-y) = x^2-y^2$

We know that a number's square is always non-negative, therefore, largest value,

$4^2-0^2=\boxed{16}$

Note : To maximize the given expression, we must maximize $x^2$ and minimize $y^2$ .

To be more specific, a REAL number's square

Kobe Cheung - 5 years, 3 months ago

Eh, there is little ambiguity since if we're working with complex numbers we're not going to be seeing $\leq$ often :)

Arthur Conmy - 3 years, 6 months ago