What is the value of base x?

Question

Given

$(135)_x+(144)_x=(323)_x$

What is the value of base $x$ ?

Answer 1

here is my solution 

Comments

I think answer will be -1 and 6 

Answer 2

SHORTCUT:

(135)_x + (144)_x = (323)_x

Just take last digit of each term and compare, 5+4=9, but it is coming as 3, so divide it by such a number so that remainder will remain 3. so, 6 is the answer. 

Answer 3

x = 6 explaination : (135)base x + (144) base x = (323)base x means... (1x^2 + 3x + 5) + (1x^2 + 4x + 4) = (3x^2 + 2x + 3) ...... then .... 2x^2 + 7x + 9 = 3x^2 + 2x + 3 x^2 - 5x - 6 = 0 ...... by division method we get ... (x-6)(x+1)=0 so .... as x must be positive ..x=6

Comments

Correct procedure.

Answer 4

X^2+3X+5+X^2+4X+4=3X^2+2X+3 which gives x=6 which is the base.