If x = 3 + √5, find the value of x + 1/x
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Answer:
x = (2 + √5)
x + 1/x
= 2 + √5 + 1/(2 + √5)
(2 + √5)² + 1/(2 + √5)
= 4 + 5 + 4√5 + 1 / (2 +√5)
= 10 + 4√5 / ( 2 + √5)
= 10 + 4√5(2 - 4√5) / 2² - √5²
= 20 -40√5 +8√5 - 90 / 4 - 5
= -70 - 32√5 / -1
= 70 + 32√5
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