SOLUTION: If x +1/x= 6, find the value of x^2 +1/x^2

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Question 1118300: If x +1/x= 6, find the value of x^2 +1/x^2
Found 2 solutions by math_helper, MathTherapy:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Ans: +highlight%28+34+%29+
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Its just a small amount of algebra and rationalization of fractions.
+x+%2B+1%2Fx+=+6+
++x%5E2-6x++=+-1+
++x%5E2-6x%2B9+=+-1+%2B+9+
++%28x-3%29%5E2+=+8+
++%28x-3%29+=+%2B-sqrt%288%29+ (*)
+blue%28+x+=+3%2Bsqrt%288%29+%29+

Considering +x=3%2Bsqrt%288%29+:
Now plug in this value of x into +x%5E2+%2B+1%2Fx%5E2+:
+%283+%2B+sqrt%288%29%29%5E2+=+9%2B6%2A%28sqrt%288%29%29%2B8+=+17%2B6sqrt%288%29+

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(*) Also, +3-sqrt%288%29+ solves x + 1/x = 6 so that number must be plugged into x^2 + 1/x^2 to get a 2nd answer. But that answer will also be +highlight%2834%29+
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Good solution @MathTherapy!

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!
If x +1/x= 6, find the value of x^2 +1/x^2
matrix%281%2C3%2C+x+%2B+1%2Fx%2C+%22=%22%2C+6%29

matrix%281%2C3%2C+x%5E2+%2B+2+%2B+1%2Fx%5E2%2C+%22=%22%2C+36%29 ------- Squaring both sides

matrix%281%2C3%2C+x%5E2+%2B+1%2Fx%5E2%2C+%22=%22%2C+36+-+2%29 

highlight_green%28matrix%281%2C3%2C+x%5E2+%2B+1%2Fx%5E2%2C+%22=%22%2C+34%29%29