if √a + √b = 2, and √a - √b = 3, what is a + b?

Answer 1

Solve the simultaneous pair by elimination of sqrt(b)

2 sqrt(a) = 5 =. sqrt(a) = 5/2 and a = 25/4

sqrt(b) = 3 - 25/4 => sqrt(b) = -1/2 => b = 1/4

therefore a + b =26/4 BUT sqrt(1/4) = 1/2 NOT -1/2 so BE CAREFUL!

Even though the values of 5/2 and -1/2 are the correct solutions of the simultaneous pair, you will introduce difficulties if you the square the results.