Please help and show steps i am very confused...
Determine a+b+c 25/84=1/a+1/ab+1/abc
First of all, you meant to say:
Determine a+b+c
if 25/84=1/a+1/ab+1/abc
Bosnian did not research on this and you might want to look at this
https://www.jiskha.com/display.cgi?id=1512455112
I still don't get it
Sure, I can help you with that. Let's break down the equation step by step:
Given the equation:
25/84 = 1/a + 1/ab + 1/abc
To determine the value of a + b + c, we need to find the values of a, b, and c first.
Let's start by simplifying the right side of the equation:
1/a + 1/ab + 1/abc
To simplify this expression, we need to find the common denominator. The least common multiple (LCM) of a, ab, and abc is simply abc.
Rewriting the expression with the common denominator, we have:
= (bc + c + 1) / abc
Now, we have the equation:
25/84 = (bc + c + 1) / abc
To simplify this equation, we can cross-multiply:
25 * abc = (bc + c + 1) * 84
Now, let's expand the right side of the equation:
25 * abc = (84bc + 84c + 84)
Next, we can simplify further:
25abc = 84bc + 84c + 84
Now, let's isolate the variables:
25abc - 84bc - 84c = 84
To find the values of a, b, and c, we can factor out the common terms:
(25ab - 84b - 84) * c = 84
Now, we have an equation in the form of (some expression) * c = 84. Since we know that c is a positive integer, we need to find the factors of 84 that satisfy this equation.
The factors of 84 are: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, and 84.
Now, substitute each factor of 84 into the equation (25ab - 84b - 84) * c = 84 to find the values of a, b, and c that satisfy the equation.
For example, let's try c = 1:
(25ab - 84b - 84) * 1 = 84
Now, we have a new equation:
25ab - 84b - 84 = 84
We can simplify this equation by moving all terms to one side:
25ab - 84b - 168 = 0
This equation is a quadratic equation in terms of b. We can solve it by factoring or using the quadratic formula.
Once you find the values of a, b, and c for each factor of 84, you can substitute them back into the original equation 25/84 = 1/a + 1/ab + 1/abc to find the value of a + b + c.
Repeat this process for each factor of 84 until you find the values of a, b, and c that satisfy the equation.
I hope this helps! Let me know if you have any further questions.