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Find a natural number whose square …

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

Posted by Siddhu Raj 6 years, 7 months ago

CBSE > Class 10 > Mathematics

1 answers

Yogita Ingle 6 years, 7 months ago

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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CBSE > Class 10 > Mathematics