Question

The difference of twu number is 8 and the difference of its squares is 208. Find the number?

Answer 1

Answer:

9 and 17

Step-by-step explanation:

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Answer 2

Answer:

17 and 9 have the difference of 8 and the difference of its squares 208.

Step-by-step explanation:

Let the numbers be x and y

Now,

According to the Question,

x - y = 8

x = y + 8 ----- 1

Also,

x² - y² = 208

Substituting eq.1 we get,

(y + 8)² - y² = 208

Using the identity, (x + y)² = x² + 2xy + y²

(y² + (2 × y × 8) + 8²) - y² = 208

y² + 16y + 64 - y² = 208

16y + 64 = 208

16(y + 4) = 208

y + 4 = 208/16

y + 4 = 13

y = 13 - 4

y = 9

Thus, from eq.1 we get,

x = 9 + 8

x = 17

Thus,

17 and 9 have the difference of 8 and the difference of its squares 208