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Given

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

What is the value of base $x$ ?
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here is my solution 

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I think answer will be -1 and

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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. 

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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

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

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