If $$a$$ and $$b$$ are numbers such that $$(a − 4)(b + 6) = 0$$, then what is the smallest possible value of $$a^2 + b^2$$ ?

Question

Uniteasy Admin · Accepted Answer

Since $$(a−4)(b+6) = 0$$, the possible solutions are:
$$ a = 4$$ and $$b$$ is anything, or $$b = −6$$ and $$a$$ is anything. 
Now, the expression$$ a^2 + b^2$$ is made smallest by choosing $$a$$ and $$b$$ to be close to zero as possible. So, $$a = 4$$ and $$b = 0$$ will give us the smallest value of $$a^2 + b^2$$, namely, 16. 
Using the other solution $$b = -6 $$ and $$a = 0$$ would give the smallest value of 36, which will be bigger than 16.
Therefore
The smallest possible value of $$a^2 + b^2$$ is $$16 $$

Question

Answer