How do you solve #13 - 3r = rsqrt5 #?

2 Answers
Alan P.
Sep 28, 2015

#r=13/(3+sqrt(5)) ~= 2.48#

Explanation:

#13-3r=rsqrt(5)#

#rarrcolor(white)("XXX")3r+rsqrt(5) =13#

#rarrcolor(white)("XXX")r(3+sqrt(5))=13#

#rarrcolor(white)("XXX")r =13/(3+sqrt(5))#

using a calculator this can be evaluated as (approximately) #2.48#

Lovecraft
Sep 28, 2015

#r = (13*(3-sqrt(5)))/(4) #

Explanation:

#13 - 3r = rsqrt(5)#
#13 = rsqrt(5) + 3r#
#13 = (3 + sqrt(5))*r#
#r = 13/(3+sqrt(5)#

Rationalizing

#r = 13/(3+sqrt(5))* (3-sqrt(5))/(3-sqrt(5)) = (13*(3-sqrt5))/(9-5) = (13*(3-sqrt(5)))/(4) #

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