A restaurant sells beverages in 16-pint pitchers. If a customer orders a pitcher of lemonade, how many gallons of lemonade does
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Answer:
a) x = (√5 -1)/2 ≈ 0.618034
b) 1/x = (√5 +1)/2 ≈ 1.618034
Step-by-step explanation:
<u>Given</u>:
x/(1 -x) = 1/x
<u>Find</u>:
Exactly, and as a decimal approximation, ...
a) x, using the quadratic formula
b) 1/x
<u>Solution</u>:
a) We can multiply the given equation by x(1 -x) to obtain ...
x² = 1 -x
x² +x -1 = 0 . . . . . . add x-1
The coefficients for use in the quadratic formula are a=1, b=1, c=-1. The solution using the quadratic formula is ...
We are only interested in the positive solution, which is ...
__
b) The quadratic we developed in the first part can be rearranged like this:
x² +x = 1 . . . . . . add 1 to both sides
x(x +1) = 1 . . . . . factor out x
x +1 = 1/x . . . . . .divide by x
Then to find the value of 1/x, we simply need to add 1 to the value of x we have: