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Date Posted: 3 years ago
Views: 222
(√5 - 2) x = √5 + 2
Multiply both sides by (√5 + 2),
(√5 + 2)(√5 - 2) x = (√5 + 2)(√5 + 2)
((√5)² - 2²)x = (√5)² + 2(√5)(2) + 2²
(5 - 4)x = 5 + 4√5 + 4
x = 9 + 4√5
Multiply both sides by (√5 + 2),
(√5 + 2)(√5 - 2) x = (√5 + 2)(√5 + 2)
((√5)² - 2²)x = (√5)² + 2(√5)(2) + 2²
(5 - 4)x = 5 + 4√5 + 4
x = 9 + 4√5
So
x + 1/x
= x²/x + 1/x
= (x² + 1)/x
= ((9 + 4√5)² + 1)/(9 + 4√5)
= (9² + 2(9)(4√5) + (4√5)² + 1)/(9 + 4√5)
= (81 + 72√5 + 4² × 5 + 1)/(9 + 4√5)
= (161 + 72√5)/(9 + 4√5)
= 18
x + 1/x
= x²/x + 1/x
= (x² + 1)/x
= ((9 + 4√5)² + 1)/(9 + 4√5)
= (9² + 2(9)(4√5) + (4√5)² + 1)/(9 + 4√5)
= (81 + 72√5 + 4² × 5 + 1)/(9 + 4√5)
= (161 + 72√5)/(9 + 4√5)
= 18
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Date Posted:
3 years ago
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