If a+b=7, and a2+b2 =25 then an=?

Solution set:  (3, 4) and (4, 3)

Step-by-step explanation:

Please, to indicate exponentiation, use " ^ ":  a^2 and b^2

Then you have:

a + b = 7 and a^2 + b^2 = 25.

Let's eliminate b:  Solve a + b = 7 for b, obtaining b = 7 - a.

Then we have:

a^2 + (7 - a)^2 = 25, or

a^2 + 49 - 14a + a^2 - 25 = 0, or

2a^2 - 14a + 24 = 0, or

a^2 - 7a + 12 = 0, which factors as follows:

(a - 3)(a - 4) = 0

This results in a = 3 and a = 4, in which case the equation a + b = 7 tells us that the b values are 4 and 3 respectively.

Solution set:  (3, 4) and (4, 3)