SOLUTION: 1+(1/x^2)=(3/x) what are the solutions to the equation? A. x=(3/2)+(square root of 5/2); x=(3/2)-(square root of 5/2) B.x=(3)+(square root of 5/2); x=(3)-(square root of 5/2) C

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Question 893870: 1+(1/x^2)=(3/x)
what are the solutions to the equation?
A. x=(3/2)+(square root of 5/2); x=(3/2)-(square root of 5/2)
B.x=(3)+(square root of 5/2); x=(3)-(square root of 5/2)
C.x=(3/2)+(square root of 13/2); x=(3/2)-(square root of 13/2)
D.x=(3)+(square root of 13/2); x=(3)-(square root of 13/2)
Answer by Theo(13342) (Show Source):
You can put this solution on YOUR website!
your equation is 1 + (1/x^2) = 3/x)

multiply both sides of the equation by x^2 to get:

x^2 + 1 = 3x

subtract 3x from both sides of the equation to get:

x^2 - 3x + 1 = 0

use the quadratic formula to solve for x.

you will get x = (3 +/- sqrt(5)) / 2

this is equivalent to x = 3/2 +/- sqrt(5)/2

that should be selection a.

the quadratic formula is:

x = -b +/- sqrt(b^2 - 4ac) ------------------------------- 2a

your formula has to be in the standard form of ax^2 + bx + c = 0
your formula is x^2 - 3x + 1 = 0
you get:
a = 1
b = -3
c = 1

replace a and b and c in the formula and solve for x.