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