Question

`(77 xx 77 xx 77 + 23 xx 23 xx 23)/(77 xx 77 - 77 xx 23 + 23 xx 23)` is equal to ______.

Options

• 90

• 100

• 110

• 120

Answer 1

`(77 xx 77 xx 77 + 23 xx 23 xx 23)/(77 xx 77 - 77 xx 23 + 23 xx 23)` is equal to 100.

Explanation:

We are asked to simplify:

`(77^3 + 23^3)/(77^2 - 77 * 23 + 23^2)`

Step 1: Recognize a sum of cubes

The numerator is a sum of cubes:

a³ + b³ = (a + b)(a² – ab + b²)

Here, a = 77 and b = 23.

Using the formula:

77³ + 23³ = (77 + 23) (77² – 77 · 23 + 23²)

Step 2: Simplify the fraction:

`(77^3 + 23^3)/(77^2 - 77 * 23 + 23^2)`

= `((77 + 23) (77^2 - 77 * 23 + 23^2))/(77^2 - 77 * 23 + 23^2)`

= 77 + 23

= 100