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Mathematics
Tomcat
20 May, 02:44
Solve 4n+2mn=3mn ² for m.
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Ace Church
20 May, 05:14
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m = sqrt (4 / (3 n) + 1 / (9 n^2)) + 1 / (3 n) or m = 1 / (3 n) - sqrt (4 / (3 n) + 1 / (9 n^2))
Step-by-step explanation:
Solve for m:
4 n + 2 m n = 3 m^2 n^2
Subtract 3 m^2 n^2 from both sides:
4 n + 2 m n - 3 m^2 n^2 = 0
Divide both sides by - 3 n^2:
m^2 - 4 / (3 n) - (2 m) / (3 n) = 0
Add 4 / (3 n) to both sides:
m^2 - (2 m) / (3 n) = 4 / (3 n)
Add 1 / (9 n^2) to both sides:
m^2 + 1 / (9 n^2) - (2 m) / (3 n) = 4 / (3 n) + 1 / (9 n^2)
Write the left hand side as a square:
(m - 1 / (3 n)) ^2 = 4 / (3 n) + 1 / (9 n^2)
Take the square root of both sides:
m - 1 / (3 n) = sqrt (4 / (3 n) + 1 / (9 n^2)) or m - 1 / (3 n) = - sqrt (4 / (3 n) + 1 / (9 n^2))
Add 1 / (3 n) to both sides:
m = sqrt (4 / (3 n) + 1 / (9 n^2)) + 1 / (3 n) or m - 1 / (3 n) = - sqrt (4 / (3 n) + 1 / (9 n^2))
Add 1 / (3 n) to both sides:
Answer: m = sqrt (4 / (3 n) + 1 / (9 n^2)) + 1 / (3 n) or m = 1 / (3 n) - sqrt (4 / (3 n) + 1 / (9 n^2))
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