Question

If a^2+b^2= 4 and ab = 5, what is the value of

(a+b)^2?
A. 10
B. 12
C. 14
D. 16

Answer 1

C. 14.

Explanation:

We use the identity:-

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

So 4 = (a + b)^2 - 2(5)

(a + b)^2 = 4 + 2(5)

= 14.

Answer 2

14

Explanation:

(a+b)^2

(a+b)(a+b)

FOIL

a^2 + ab+ab + b^2

Combine like terms

a^2 +2ab + b^2

Rearranging

a^2+b^2 +2ab

We know a^2+b^2 = 4 and ab= 5

4 + 2(5)

4+10

14