Given 3 (square root 2m - n) = k
Express m in terms of k and n
3√(3m-n) = k
9(3m-9) = k^2
3m-9 = k^2/9
3m = k^2/9 + 9
m = k^2/27 + 3
oops. lost the n
3m-n = k^2/9
3m = k^2/9 + n
m = k^2/27 + n/3
or m = (k^2 + 9n)/27
To express m in terms of k and n, you can follow the steps below:
Step 1: Start with the equation:
3√(2m - n) = k
Step 2: Isolate the square root term by dividing both sides of the equation by 3:
√(2m - n) = k/3
Step 3: Square both sides of the equation to eliminate the square root:
(√(2m - n))^2 = (k/3)^2
Step 4: Simplify the equation by squaring both sides:
2m - n = k^2/9
Step 5: Now, isolate m by adding n to both sides of the equation:
2m = n + k^2/9
Step 6: Finally, solve for m by dividing both sides of the equation by 2:
m = (n + k^2/9) / 2
Therefore, m can be expressed in terms of k and n as:
m = (n + k^2/9) / 2