Question #70e44

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Question #70e44

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Answer 1 · 2017-04-16T14:51:59

$x in {+5, +2}$

Explanation:

Case $1$ : the absolute value is positive

$3m = m^2 - 10$

$0 = m^2 - 3m - 10$

$0 = (m - 5)(m + 2)$

$m = 5 or -2$

Case $2$ : the absolute value is negative

$3m = -(m^2 - 10)$

$3m = -m^2 +10$

$m^2 + 3m - 10 = 0$

$(m + 5)(m - 2) = 0$

$m = -5 or 2$

However, the negative solutions are extraneous because the left hand side would be negative while the right hand side would be positive (by the definition of $|a|$ ).

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Question #70e44

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