Question

If ab = 9 and a² + b² = 81, then (a+b)² = ?​

Answer 1

Answer:

99

Step-by-step explanation:

Through some clever algebra, we can combine our first two equations using the fact that

$(a+b)^2=a^2+2ab+b^2$

We have the a² and the b² in the equation $a^2+b^2=81$, and we almost have a 2ab in the equation $ab=9$. To get that 2ab, we can simply double both sides of the first equation to get $2ab=18$. From there, we'll add the first two equations together, giving us the summed equation

$a^2+b^2+2ab=81+18\\a^2+2ab+b^2=99$

And since $(a+b)^2=a^2+2ab+b^2$, we can equivalently say that

$(a+b)^2=99$