Question

solve:
$6m {}^{2} + \frac{2}{m {}^{2} } = 7$
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Answer 1

Answer:

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Answer 2

$6 {m}^{2} + \frac{2}{ {m}^{2} } = 7 \\ 6 {m}^{2} + \frac{2}{ {m}^{2} } - 7 = 0 \\ \\ multiplying \: throughout \: by \: {m}^{2} \\ {6m}^{4} + 2 - 7 {m}^{2} = 0 \\ 6 {(m {}^{2})}^{2} - 7 {m}^{2} + 2 = 0 \\ \\ let \: {m}^{2} = x \\ \\ then \\ 6 {x}^{2} - 7x + 2 = 0 \\ 6 {x}^{2} - 3x - 4x + 2 = 0 \\ 3x(2x - 1) - 2(2x - 1) = 0 \\ (3x - 2)(2x - 1) = 0 \\ 3x - 2 = 0 \: \: or \: \: 2x - 1 = 0 \\ x = \frac{2}{3} \: \: or \: \: x = \frac{1}{2} \\ {m}^{2} = \frac{2}{3 } \: \: or \: \: {m}^{2} = \frac{1}{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: ( {m}^{2} = x) \\ m = \sqrt{ \frac{2}{3} } \: \: or \: m = \frac{1}{ \sqrt{2} }$