If a²-30+1=0, find a² + 1/a²
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a² - 3a -1= 0
a² - 1 = 3a
(a² - 1)/a = 3a/a. {dividing the equation by a}
a - 1/a = 3
a² + 1/a² - 2 = (a-1/a)²
a² + 1/a² - 2 = (3)²
a² + 1/a² - 2 = 9
a² + 1/a² = 11
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