How do you solve x+1/x=7?

2 Answers
May 25, 2018

color(red)(x=3.85 or 0.15

Explanation:

x+1/x=7

or, x+1/x-7=0

or, (x^2+1-7x)/x=0

or, x^2-7x+1=0

or, x=(-(-7)+-sqrt((7^2)-4*1))/(2*1)=(7+-sqrt45)/2=(7+-3sqrt5)/2

therefore x=3.5+1.5sqrt5 or 3.5-1.5sqrt5

or, x=3.5+3.35 or 3.5-3.35

or, x=3.85 or 0.15

May 25, 2018

x=7/2+-3/2sqrt5

Explanation:

"multiply through by "x

x^2+1=7x

"arrange in "color(blue)"standard form ";ax^2+bx+c=0

"subtract "7x" from both sides"

x^2-7x+1=0

"check the value of the "color(blue)"discriminant"

•color(white)(x)Delta=b^2-4ac

"with "a=1,b=-7" and "c=1

b^2-4ac=(-7)^2-(4xx1xx1)=45

"thus the roots are real and irrational"

"solve using the "color(blue)"quadratic formula"

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

x=(7+-sqrt45)/2=(7+-3sqrt5)/2

x=7/2+-3/2sqrt5larrcolor(red)"exact solutions"