How do you solve x+1/x=7?
2 Answers
May 25, 2018
Explanation:
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May 25, 2018
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"