Question

the difference of two numbers is 5 and the difference of their square is 135. The sum of the numbers is _______

Answer 1

the answer is 27
hope it helps you....
process
135/5=27

Answer 2

Required sum of two numbers is 27.

Let the two numbers be p, q.

According to the question,

Difference of the numbers is 5

⇒ p - q = 5

Difference of squares of the numbers is

⇒ p² - q² = 135

By Algebraic identity

${x}^{2} - {y}^{2} = (x + y)(x - y)$

Now,

${p}^{2} - {q}^{2} = (p + q)(p - q) \\ \\ 135 = 5(p + q) \\ \\ p + q = \frac{135}{5} \\ \\ p + q = 27$

Therefore, The sum of the numbers is 27

We can further find the numbers too

⇒ p + q = 27

⇒ p - q = 5

Adding both equations gives,

⇒ 2p = 32

⇒ p = 16

Subtracting both equations gives,

⇒ 2q = 22

⇒ q = 11.