the sum of a number and its reciprocal is 8. Find its number?

Answer 1

x+1/x = 8
multiply everything by x gives: x^2+1=8x
bring everything to one side = x^2-8x+1 = 0
At this point use the quadratic equation to solve for x.
(quadratic equation says that a polynomial in the form of ax^2 + bx + c =0, then x = (-b plus or minus the square root of (b^2 - 4ac) all devided by 2a.
In this case, 8 plus or minus the sqaure root of 60 all divided by 2.

Answer 2

Let x be the unknown number. Then x + 1/x = 8. Multiplying through by x gives us x^2 + 1 = 8x, or x^2 - 8x +1 = 0. Use the Quadratic formula to find that x = 4 +- sq rt (15).

Answer 3

Let the number is x.
x + 1/x = 8
Multiply both sides by x,
x^2 + 1 = 8x
x^2 - 8x + 1 = 0
Using a formula, you got :
x1,2 = {-8 +- root of [(-8)^2 - 4*1*1]}/2
= {-8 +- root of [64 - 4]}/2
= {-8 +- 2*root of (15)}/2
= -4 +- root of (15)
So, it could be : - 4 + root of 15, or
- 4 - root of 15.

Answer 4

let it is x ,then x +1/x = 8
then x^2- 8x + 1=0 , using the formula x=[-b±√(b²-4ac)] /(2a)
then x =4 ±√15