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

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Sum

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

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Solution

Let the natural number = ‘x’.

According to the question,

We get the equation,

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

Since, natural numbers cannot be negative.

The number is 12.

Concept: Nature of Roots
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APPEARS IN

NCERT Mathematics Exemplar Class 10
Chapter 4 Quadatric Euation
Exercise 4.4 | Q 2 | Page 42
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