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Allyson Booker
Mathematics
26 November, 08:22
Evaluate the equation 4K-10/k=8
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Grady Lamb
26 November, 08:45
0
k = 1 + sqrt (7/2) or k = 1 - sqrt (7/2)
Step-by-step explanation:
Solve for k over the real numbers:
4 k - 10/k = 8
Bring 4 k - 10/k together using the common denominator k:
(2 (2 k^2 - 5)) / k = 8
Multiply both sides by k:
2 (2 k^2 - 5) = 8 k
Expand out terms of the left hand side:
4 k^2 - 10 = 8 k
Subtract 8 k from both sides:
4 k^2 - 8 k - 10 = 0
Divide both sides by 4:
k^2 - 2 k - 5/2 = 0
Add 5/2 to both sides:
k^2 - 2 k = 5/2
Add 1 to both sides:
k^2 - 2 k + 1 = 7/2
Write the left hand side as a square:
(k - 1) ^2 = 7/2
Take the square root of both sides:
k - 1 = sqrt (7/2) or k - 1 = - sqrt (7/2)
Add 1 to both sides:
k = 1 + sqrt (7/2) or k - 1 = - sqrt (7/2)
Add 1 to both sides:
Answer: k = 1 + sqrt (7/2) or k = 1 - sqrt (7/2)
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