If 314\(_{10}\) – 256\(_7\) = 340\(_x\), find x.

Explanation

\(314_{10} - 256_7 = 340_x\)
Convert 2567 and 340x to base 10, such that:
314 - 139 = 3x\(^2\) + 4x
=> \(3x^2\) + 4x - 175 = 0 (quadratic)
Factorising, (x - 7) (3x + 25) = 0,
either x = 7 or x = -25/3 ( but x cannot be negative)

Therefore, x = 7.

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