Question
Equation: 4//n=1//a+1//b+1//c where n >= 2 a,b and c are positive integers.
Answer
4.6
(302 Votes)
Kendra
Professional · Tutor for 6 years
Answer
`n = 4abc / (bc + ac + ab)`.
Explanation
This problem falls under the domain of 'Rational Equations'. In order to find the values of a, b and c, we must use the properties of fractions and manipulate the provided equation accordingly, following these steps:Step 1: Rewrite the equation: The provided equation `4/n = 1/a + 1/b + 1/c`, can be mathematically rewritten as `4/n = (bc + ac + ab) / abc`Step 2: Ensure equivalent fractions: By cross multiplying, we obtain `4abc = n(bc + ac + ab)`Step 3: Rearrange the elements: This can be rewritten as (`4abc = nabc`)Please note, the values of a, b, c and n should satisfy this equation and be positive, whole numbers. The equation also provides information they are not decimal point values or negative integers. Observe that according to the conditions provided, n≥2 which imply abc would be twice or more than twice the provided value.