If (x+6)/x^(1/2) = 35 then what is the value of (x+1)/x ?

2 Answers
Feb 22, 2018

1

Explanation:

Solve for x:

(x+6)/x^(1/2)=35
x+6=35x^(1/2)

I chose to square both sides in order to get rid of the square root.

(x+6)^2=1225x
x^2+12x+36=1225x
x^2-1213x+36=0

I don't think I can factor this, so I'm going to apply the quadratic formula instead!

x=(-b+-sqrt(b^2-4ac))/(2a)
x=(1213+-5sqrt(58849))/2
x=(1213+5sqrt(58849))/2 because (((1213+5sqrt(58849))/2)+6)/sqrt((1213+5sqrt(58849))/2)=35

Now all you have to do is plug x=(1213+5sqrt(58849))/2 into (x+1)/x!

(x+1)/x~~1

Feb 22, 2018

(x+1)/x = 1285/72+-35/72sqrt(1201)

Explanation:

Given:

(x+6)/x^(1/2) = 35

Multiply both sides by x^(1/2) to get:

x+6 = 35x^(1/2)

Square both sides to get:

x^2+12x+36 = 1225x

Subtract 1225x from both sides to get:

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 1/x^2 we get:

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)