If (x+6)/x^(1/2) = 35 then what is the value of (x+1)/x ?
2 Answers
1
Explanation:
Solve for x:
I chose to square both sides in order to get rid of the square root.
I don't think I can factor this, so I'm going to apply the quadratic formula instead!
Now all you have to do is plug
Explanation:
Given:
(x+6)/x^(1/2) = 35
Multiply both sides by
x+6 = 35x^(1/2)
Square both sides to get:
x^2+12x+36 = 1225x
Subtract
x^2-1213x+36 = 0
Next note that we want to find:
(x+1)/x = 1+1/x
Multiplying the quadratic we have found by
36(1/x)^2-1213(1/x)+1 = 0
So by the quadratic formula we find:
1/x = (1213+-sqrt((-1213)^2-4(36)(1)))/(2(36))
color(white)(1/x) = (1213+-sqrt(1471369-144))/72
color(white)(1/x) = (1213+-sqrt(1471225))/72
color(white)(1/x) = (1213+-35sqrt(1201))/72
So:
(x+1)/x = 1+1/x = 1285/72+-35/72sqrt(1201)