SOLUTION: I'm homeschooled, and I've been working on this problem for a long time. My mother gave me the answer, but I can't seem to work the steps out. The question is: What are the sol

Algebra ->  Equations -> SOLUTION: I'm homeschooled, and I've been working on this problem for a long time. My mother gave me the answer, but I can't seem to work the steps out. The question is: What are the sol      Log On


   

Question 422034: I'm homeschooled, and I've been working on this problem for a long time. My mother gave me the answer, but I can't seem to work the steps out.
The question is:
What are the solutions to the equation 1 + (1/x^2) = (3/x).
The answer is:
x = (3/2) + ((sqrt 5)/2); x = (3/2) - ((sqrt5)/2)
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
1+%2B+1%2Fx%5E2+=+3%2Fx Start with the given equation.


x%5E2+%2B+1+=+3x Multiply EVERY term by the LCD x%5E2 to clear out the fractions.


x%5E2-3x%2B1=0 Subtract 3x from both sides.


Notice that the quadratic x%5E2-3x%2B1 is in the form of Ax%5E2%2BBx%2BC where A=1, B=-3, and C=1


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%28-3%29+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Plug in A=1, B=-3, and C=1


x+=+%283+%2B-+sqrt%28+%28-3%29%5E2-4%281%29%281%29+%29%29%2F%282%281%29%29 Negate -3 to get 3.


x+=+%283+%2B-+sqrt%28+9-4%281%29%281%29+%29%29%2F%282%281%29%29 Square -3 to get 9.


x+=+%283+%2B-+sqrt%28+9-4+%29%29%2F%282%281%29%29 Multiply 4%281%29%281%29 to get 4


x+=+%283+%2B-+sqrt%28+5+%29%29%2F%282%281%29%29 Subtract 4 from 9 to get 5


x+=+%283+%2B-+sqrt%28+5+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%283%2Bsqrt%285%29%29%2F%282%29 or x+=+%283-sqrt%285%29%29%2F%282%29 Break up the expression.


So the solutions are x+=+%283%2Bsqrt%285%29%29%2F%282%29 or x+=+%283-sqrt%285%29%29%2F%282%29


If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
What are the solutions to the equation 1 + (1/x^2) = (3/x).
Multiply thru by x^2 to get rid of the denominators:
x^2 + 1 = 3x
---
Rearrange:
x^2-3x+1 = 0
-----
Use the quadratic formula to get:
x = [3 +- sqrt(9-4*1)]/2
---
x = [3 +- sqrt(5)]/2
===
x = (3/2)+(1/2)sqrt(5) or x = (3/2)-(1/2)sqrt(5)
===================================================
Cheers,
Stan H.
============