+50 Work out the width of a rectangle with area √5 and length 1+√5.
Give your answer in the form a+b√5, where a and b are rational constants
Simplify the following:
(sqrt(5))/(1+sqrt(5))
Multiply numerator and denominator of (sqrt(5))/(1+sqrt(5)) by sqrt(5)-1:
(sqrt(5) (sqrt(5)-1))/((1+sqrt(5)) (sqrt(5)-1))
(1+sqrt(5)) (sqrt(5)-1) = -1+1 sqrt(5)-sqrt(5)+sqrt(5) sqrt(5) = -1+sqrt(5)-sqrt(5)+5 = 4:
(sqrt(5) (sqrt(5)-1))/(4)
sqrt(5) (sqrt(5)-1) = 5-sqrt(5):
Answer: |5/4 - sqrt(5)/4
