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Q.

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


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a

12

b

9

c

-9

d

-12 

answer is A.

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Detailed Solution

It is given, a natural number whose square diminished by 84 is equal to thrice of 8 more than the number.
Let the natural number be x.
⇒ x 2 −84=3(x+8)  
⇒ x 2 −84=3x+24  
⇒ x 2 −3x−84−24=0  
⇒ x 2 −3x−108=0   ⇒ x 2 −12x+9x−108=0  
⇒ x(x−12)+9(x−12)=0  
⇒ (x−12)(x+9)=0  
Therefore, two values of x are
⇒x=12 or x=−9
x=−9 is not a natural number so it can be ignored.
Therefore, the correct option is 1.
 
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