Question

the sum of a natural number and its square is 156 find the number

Answer 1

Hey there !

Thanks for the question !

Solution:

Let the given number be 'x'

According to the question,

=> x + x² = 156

=> x² + x - 156 = 0

Factorizing the above equation we get,

=> x² + 13 x - 12 x - 156 = 0

=> x ( x + 13 ) - 12 ( x + 13 ) = 0

=> ( x - 12 ) ( x + 13 ) = 0

=> x = 12, ( -13 )

Since the given number is a natural number, the number can only be positive. Hence -13 can be neglected.

Hence we get x = 12

Hence the unknown number 'x' is 12.

Hope my answer helped !

Answer 2

Let the no be x
The sum of the no. itself and it's square is 156

Thus
x² + x = 156
x² + x - 156 = 0
x² + 13x - 12x - 156 = 0
x(x + 13) - 12(x + 13)
(x + 13)(x - 12) = 0
x = -13 OR x = 12

but the no is natural no and thus it can't be negative

thus x = 12

THE REQUIRED NO IS 12


VERIFICATION:-
x² + x = 156
(12)² + 12 = 156
144 + 12 = 156
156 = 156
LHS = RHS

THUS 12 IS THE CORRECT ANS !!!