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Given that $(292)_{10} = (1204)_x$ in some number system $x$. The base $x$ of that number system is

1. 2
2. 8
3. 10
4. None of the above
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(292)10=(1204)x

2*10+ 9*10 + 2 = x+ 2*x2 + 0 + 4

200 + 90 + 2 = x3 + 2x2 + 4

x3 + 2x2 - 288 = 0

solution for x = 6

none of the option satisfy the equation.

selected

(1204) x = 1*x 3 + 2* x 2 + 0 * x + 4 = x3+2x2+4=292

x3+2x2=288

x2(x+2) = 288

//Rather than solving x, it will be easier to check given options. In time stringent exams, this approach will behelpful

A. 2 2 (2+2) = 4* 6=24 ≠ 288

B. 8 2 (8+2) =64*100 =6400≠ 288

C. 10 2 (10+2) =100*12 =1200 ≠ 288

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