Question

Find a natural number whose square diminished by 10 is equal to five times of 8 more than the given number

Answer 1

The natural number is 10.

Step-by-step explanation:

Let the natural number is x.

So, the square of x diminished by 10 will be (x² - 10).

And five times of 8 more than x will give 5(x + 8).

If they are equal then we can write that, (x² - 10) = 5(x + 8)

⇒ x² - 10 = 5x + 40

⇒ x² - 5x - 50 = 0

⇒ x² - 10x + 5x - 50 = 0

⇒ (x - 10)(x + 5) = 0

⇒ x = 10 or - 5.

But, x is a natural number and x can not be negative, so, x = 10

Therefore, the natural number is 10. (Answer)

Answer 2

Given :

• A natural number diminished by 10 is equal to five times of 8 more than the given number.

ㅤㅤ

Find :

• Find the natural number.

ㅤㅤ

Calculations :

→ x - 84 = 3 (x + 8)

→ x - 84 = 3x + 24

→ x - 3x - 84 - 24 = 0

→ x - 12x + 9x - 108 = 0

→ (x + 9) (x - 12)

→ (x = -9) , (x = 12)

ㅤㅤ

Therefore, 12 is the natural number.

ㅤㅤ

♦ Remember that, natural number can't be in negative, hence (12 is the natural number).

ㅤㅤ

Additional information :

• Natural numbers are the numbers who start from the positive integers and go beyond infinite.

ㅤㅤ

• On number line there are two sets of numbers (Integers).

ㅤㅤ

1. Positive integers.
2. Negative integers.

ㅤㅤ

• The postive integers lie on the left side of the number lie and the negative integers lie on the right side of the number lie.

ㅤㅤ

• Only the number (zero) is neither a postive integer nor a negative integer.

ㅤㅤ

This concept is undergone into the chapter of Integers.