If (a + b)2 = 49, and ab = 10, which of the following represents the value of b in terms of a?

If  (a + b)^2  = 49......then either

a + b  = 7               or          a +  b  =  -7

b = 7 - a                or           b = -7 - a

And if ab  = 10, then either

a(7 - a)  = 10        or        a (-7 - a)  = 10

7a - a^2  = 10      or        -7a - a^2  = 10    

Rearrange both as

a^2 - 7a + 10  = 0            or            a^2 + 7a + 10 = 0

Factor

(a - 5) (a -2)  = 0            or            (a + 5) (a + 2)  = 0

Setting each factor to 0, a takes on 4 values

a = -5, -2, 2 or 5

And using ab = 10, b = 10/a....so.......b = -10/5, 10/-2, 10/2 or 10/5   .......   and these values are b in terms of the value for a

a = 1/4 (49-3 sqrt(249)) = 0.415200 and b = 1/4 (49+3 sqrt(249)) = 24.0848

a = 1/4 (49+3 sqrt(249)) = 24.0848 and b = 1/4 (49-3 sqrt(249)) = 0.415200

If (a + b)² = 49 then a + b = 7  or  a + b = -7

so b = 7 - a   (1)   or b = -7 - a  (2)

using (1):   a*(7 - a) = 10  so a² - 7a + 10 = 0   or (a - 5)(a - 2) = 0  so a = 5 (and b = 2) or a = 2 (and b = 5)

See if you can repeat the process using (2).

Edited to correct stupid misprint!