Question

If the sum of a number and its square is 992 what is the number

Answer 1

Heya user,

Let the no. be x..
Given, x² + x = 992

If x is three digit no. x² > 10000
.'. x is a two digit no.

Now, if x > 31, x² > 961
And x (max) = 99

.'. we find a no. whose square is nearest to 992 ...
Also, x²(min) = 992 - 99 = 902

Such a no. is 31... Also, verifying our result, 31²  + 31 = 992

Hence, our req.d no. is 31...... 
Note: This method is applicable not for boards and only for +ve Z.

  OR you can do....

x² + x = 992
=> x² + x - 992 = 0
=> ( x - 31 ) ( x + 32 ) = 0
=> x = 31, -32 ... 
Hence the no.s are -32 and 31