Given that ##a-b=10## and that ##2 * (a+b)^2=64##, what is the value of ##a+b## ?

##a+b = +-4sqrt(2)##

Given that:

##2*(a+b)^2 = 64##

Divide both sides by ##2## to find:

##(a+b)^2 = 32##

Hence:

##a+b = +-sqrt(32) = +-sqrt(4^2*2) = +-4sqrt(2)##

##color(white)()##Bonus

Given:

##a-b=10##

##a+b=+-4sqrt(2)##

Adding these two equations, we find:

##2a = 10+-4sqrt(2)##

So ##a = 5+-2sqrt(2)##

Then ##b = a-10 = -5+-2sqrt(2)##

That is, the two possible solutions are:

##(a, b) = (5+2sqrt(2), -5+2sqrt(2))##

##(a, b) = (5-2sqrt(2), -5-2sqrt(2))##