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Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number

Solution:

Given, a natural number’s square diminished by 84 is equal to thrice of 8 more than the given number.

We have to find the natural number.

Let the natural number be x.

So, x² - 84 = 3(x + 8)

x² - 84 = 3x + 24

x² - 3x - 24 - 84 = 0

x² - 3x - 108 = 0

x² - 12x + 9x - 108 = 0

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

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

Now, x + 9 = 0

x = -9

Also, x - 12 = 0

x = 12.

Since a natural number cannot be negative, x = -9 is neglected.

Therefore, the natural number is x = 12.

✦ Try This: Find a natural number whose square diminished by 4 is equal to thrice of 9 more

than the given number

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 4

NCERT Exemplar Class 10 Maths Exercise 4.4 Problem 2

Summary:

A natural number whose square diminished by 84 is equal to thrice of 8 more than the given number is 12

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