• ### If a + 1/a = 10, find |a² + 1/(a²)|?

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 *... show more
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 · 14 hours ago
• ### Selecting 2 balls. What is the probability of selecting 2 blue balls out of 10 blue balls and 5 red balls?

4 answers · 2 hours ago
• ### Math..........?

5 answers · 17 hours ago
• ### What is 10 percent of 92.99 pounds?

9 answers · 3 hours ago
• ### Help with hypotenuse?

How can I find h in this picture?
How can I find h in this picture?
9 answers · 2 days ago
• ### 20/24 +5/8=?

17 answers · 3 days ago
• ### Im building a door, the door however needs to be on a lean to fit into the doorway. What is the angle? or how do i figure it out.?

Length of door itself: 143.5cm Width of door itself: 68.5cm Finding: Angle that the door needs to be on to fit into the doorway. (the door will be a parallelogram)
Length of door itself: 143.5cm Width of door itself: 68.5cm Finding: Angle that the door needs to be on to fit into the doorway. (the door will be a parallelogram)
5 answers · 3 days ago
• ### One fifth plus thirty three divided by one fifth?

16 answers · 3 days ago
• ### Need Help with this equation 2/5 + p = 4/5 + 3/5p?

17 answers · 4 days ago
• ### How do I integrate ∫dx/(8+3x)?

How do I integrate ∫(dx/(8+3x)) I have a general idea, u-substitution... My final answer gets pretty close, but isn't exact to the right answer. Someone people help me a (desperate student)!!! thanks, much appreciated!
How do I integrate ∫(dx/(8+3x)) I have a general idea, u-substitution... My final answer gets pretty close, but isn't exact to the right answer. Someone people help me a (desperate student)!!! thanks, much appreciated!
10 answers · 1 day ago
• ### Math Help?

119.99 + ((230 - 100) X 0.31)

119.99 + 40.30 = 160.29

119.99 + ((230 - 100) X 0.31)

119.99 + 40.30 = 160.29
10 answers · 2 days ago
• ### Is it possible that humans orignially evolved from mushrooms?

6 answers · 1 hour ago
• ### If cosθ is equal to 90°, what is the value of cosθ?

11 answers · 2 days ago
• ### If (2x+1/3x)=6 what is the value of (3x-1/2x)^2?

7 answers · 1 day ago
• ### How do you solve this radical equation?

2√(x+2) -√(x-3) =√(x+9)
2√(x+2) -√(x-3) =√(x+9)
9 answers · 2 days ago
• ### What is a positive times a positive?

9 answers · 2 days ago
• ### Solve 0.5e^0.92t=0?

I doubt it.

~Peanuts2345
I doubt it.

~Peanuts2345
7 answers · 19 hours ago
• ### HOW MUCH IN 78 ROLLS OF QUARTERS?

7 answers · 23 hours ago
• ### What fraction of an inch .185?

11 answers · 3 days ago
• ### Evaluate the following function?

Evaluate the following function at the values t + 2 and t + h. g(t) = 3t^3 - 7t g(t+2)=? g(t+h)=?
Evaluate the following function at the values t + 2 and t + h. g(t) = 3t^3 - 7t g(t+2)=? g(t+h)=?
5 answers · 4 days ago