Question

If a-b = 2, ab=15, find: a+b

Answer 1

Given: $a-b=2,\;ab=15$

To find: the value of $a+b$

Solution:

• Before solving the problem, we must know algebraic identity as follows,
• $(a+b)^{2}=(a-b)^{2}+4ab$

• Now putting $a-b=2$ and $ab=15$ in the above formula, we get
• $\quad (a+b)^{2}=2^{2}+4\times 15$
• $\Rightarrow (a+b)^{2}=4+60$
• $\Rightarrow (a+b)^{2}=64$
• $\Rightarrow (a+b)^{2}=8^{2}$
• $\Rightarrow a+b=8$

• Note: since the left hand side contains a perfect square $(a+b)^{2}$, it cannot be negative. So we take $(+8)$ as the required value.

Answer: the value of $a+b$ is $8$.