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

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Feb 22, 2018

Answer:

#(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)#

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Dani W. Share
Feb 22, 2018

Answer:

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#

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