SOLUTION: Can you please help me with this problem: The sum of two numbers is four and their product is one. Find the sum of their cubes. I tried it this way, 4(x+4-4)=1. I got an answer but

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Question 578601: Can you please help me with this problem: The sum of two numbers is four and their product is one. Find the sum of their cubes. I tried it this way, 4(x+4-4)=1. I got an answer but when I checked it by using my answers I got wrong ones. Can you please help me, this will serve as an opportunity for me to solve more problems like these. Thank you so much!
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The sum of two numbers is four
a + b = 4
a = (4-b)
:
and their product is one.
a * b = 1
replace a with (4-b)
(4-b)*b = 1
-b^2 + 4b - 1 = 0
Use the quadratic formula to find b
b+=+%28-4+%2B-+sqrt%284%5E2-4%2A-1%2A-1+%29%29%2F%282%2A-1%29+
b+=+%28-4+%2B-+sqrt%2812+%29%29%2F%28-2%29+
two solutions:
b = %28-4+%2B+3.464%29%2F%28-2%29+
b = %28-.5358%29%2F%28-2%29
b = +.268, then a = 3.732
and
b+=+%28-4+-+3.464%29%2F%28-2%29+
b = %28-7.464%29%2F%28-2%29
b = +3.732, then a = .268
:
Find the sum of their cubes.
.268^3 + 3.732^3 ~ 52