Question

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

Answer 1

Let the natural number be 'x'.

Therefore, according to the question.

x² - 84 = 3(x+8)

x² - 84 = 3x + 24

x² - 3x - 84 - 24 = 0

x² - 3x - 108 = 0

x² - 12x + 9x - 108 = 0

x(x - 12) + 9(x - 12) = 0

(x + 9) (x - 12)

⇒ x = -9 and x = 12

We have to take the positive value because natural numbers cannot be negative. 

Therefore, the number is 12

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Answer 2

Given :

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

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Find :

Find the natural number.

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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)

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Therefore, 12 is the natural number.

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

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Additional information :

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

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

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• Positive integers.

• Negative integers.ㅤㅤ

3) 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.

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