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Find the sum

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Joined: 25 Nov 2017
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Find the sum [#permalink]

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New post 25 Nov 2017, 10:07
Find the sum of all solutions of
3|2 − x|^2 − 7|x − 2| =6

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Re: Find the sum [#permalink]

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New post 28 Nov 2017, 10:16
Nawarashraf wrote:
Find the sum of all solutions of
3|2 − x|^2 − 7|x − 2| =6

Posted from my mobile device


\(3|2 − x|^2 − 7|x − 2| = 6\)
\(3|x-2|^2 - 7|x-2| - 6 = 0\)
\((3|x-2|+2)(|x-2|-3) = 0\)
\(3|x-2| + 2 = 0\) or \(|x-2| = 3\).
Since we have \(|x-2|≥0\) and \(3|x-2| + 2≥2>0\), \(3|x-2| + 2 ≠ 0\).

From \(|x-2| = 3\), we have \(x - 2 = ±3\).
\(x = 2 ± 3\).
\(x = 5\) or \(-1\).
Thus the sum of solutions is \(5 + (-1) = 4\).
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Re: Find the sum   [#permalink] 28 Nov 2017, 10:16
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Find the sum

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