Best answer:
(a + 1/a) = 10
(a + 1/a)^2 = 10^2
a^2 + 2 * a * (1/a) + 1/a^2 = 100
a^2 + 2 * 1 + 1/a^2 = 100
a^2 + 1/a^2 = 100 - 2
a^2 + 1/a^2 = 98
Or we could solve for a to begin with and work from there
a + 1/a = 10
a^2 + 1 = 10a
a^2 - 10a = -1
a^2 - 10a + 25 = 25 - 1
(a - 5)^2 = 24
a - 5 = +/- 2 * sqrt(6)
a = 5 +/- 2 *...
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Best answer: (a + 1/a) = 10
(a + 1/a)^2 = 10^2
a^2 + 2 * a * (1/a) + 1/a^2 = 100
a^2 + 2 * 1 + 1/a^2 = 100
a^2 + 1/a^2 = 100 - 2
a^2 + 1/a^2 = 98
Or we could solve for a to begin with and work from there
a + 1/a = 10
a^2 + 1 = 10a
a^2 - 10a = -1
a^2 - 10a + 25 = 25 - 1
(a - 5)^2 = 24
a - 5 = +/- 2 * sqrt(6)
a = 5 +/- 2 * sqrt(6)
a^2 = (5 +/- 2 * sqrt(6))^2
a^2 = 25 +/- 20 * sqrt(6) + 24
a^2 = 49 +/- 20 * sqrt(6)
a^2 + 1/a^2 =>
49 + 20 * sqrt(6) + 1/(49 + 20 * sqrt(6)) , 49 - 20 * sqrt(6) + 1/(49 - 20 * sqrt(6))
49 + 20 * sqrt(6) + (49 - 20 * sqrt(6)) / (49^2 - 400 * 6) , 49 - 20 * sqrt(6) + (49 + 20 * sqrt(6)) / (49^2 - 400 * 6)
49 + 20 * sqrt(6) + (49 - 20 * sqrt(6)) / (2401 - 2400) , 49 - 20 * sqrt(6) + (49 + 20 * sqrt(6)) / (2401 - 2400)
49 + 20 * sqrt(6) + (49 - 20 * sqrt(6)) / 1 , 49 - 20 * sqrt(6) + (49 + 20 * sqrt(6)) / 1
49 + 20 * sqrt(6) + 49 - 20 * sqrt(6) , 49 - 20 * sqrt(6) + 49 + 20 * sqrt(6)
98 + 0 * sqrt(6) , 98 + 0 * sqrt(6)
98 , 98
Again, we have 98. Which method did you like better
8 answers
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2 days ago