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x+1/x=25   x^2+1/x^2=?

 Feb 13, 2016

Best Answer 

 #1
avatar
+5

x+1/x=25

 

Solve for x:

x+1/x = 25

Bring x+1/x together using the common denominator x:

(x^2+1)/x = 25

Multiply both sides by x:

x^2+1 = 25 x

Subtract 25 x from both sides:

x^2-25 x+1 = 0

Subtract 1 from both sides:

x^2-25 x = -1

Add 625/4 to both sides:

x^2-25 x+625/4 = 621/4

Write the left hand side as a square:

(x-25/2)^2 = 621/4

Take the square root of both sides:

x-25/2 = (3 sqrt(69))/2 or x-25/2 = -(3 sqrt(69))/2

Add 25/2 to both sides:

x = 25/2+(3 sqrt(69))/2 or x-25/2 = -(3 sqrt(69))/2

Add 25/2 to both sides:

Answer: |x = 25/2+(3 sqrt(69))/2                  or              x = 25/2-(3 sqrt(69))/2

 

 x^2+1/x^2=?

Simplify the following:

x^2+1/x^2

Put each term in x^2+1/x^2 over the common denominator x^2: x^2+1/x^2 = x^4/x^2+1/x^2:

x^4/x^2+1/x^2

x^4/x^2+1/x^2 = (x^4+1)/x^2:

Answer: |(x^4+1) / x^2

 Feb 13, 2016
 #1
avatar
+5
Best Answer

x+1/x=25

 

Solve for x:

x+1/x = 25

Bring x+1/x together using the common denominator x:

(x^2+1)/x = 25

Multiply both sides by x:

x^2+1 = 25 x

Subtract 25 x from both sides:

x^2-25 x+1 = 0

Subtract 1 from both sides:

x^2-25 x = -1

Add 625/4 to both sides:

x^2-25 x+625/4 = 621/4

Write the left hand side as a square:

(x-25/2)^2 = 621/4

Take the square root of both sides:

x-25/2 = (3 sqrt(69))/2 or x-25/2 = -(3 sqrt(69))/2

Add 25/2 to both sides:

x = 25/2+(3 sqrt(69))/2 or x-25/2 = -(3 sqrt(69))/2

Add 25/2 to both sides:

Answer: |x = 25/2+(3 sqrt(69))/2                  or              x = 25/2-(3 sqrt(69))/2

 

 x^2+1/x^2=?

Simplify the following:

x^2+1/x^2

Put each term in x^2+1/x^2 over the common denominator x^2: x^2+1/x^2 = x^4/x^2+1/x^2:

x^4/x^2+1/x^2

x^4/x^2+1/x^2 = (x^4+1)/x^2:

Answer: |(x^4+1) / x^2

Guest Feb 13, 2016
 #2
avatar+8645 
+5

Hallo Gast!

 

x+1/x=25

 

x² + 1 = 25x

x² - 25x + 1 = 0

x1;2 = 12.5 +- √(12.5² - 1)

x1 = 24.96

x2 = 0.0401

 

 

x^2+1/x^2=?

 

x² + 1/x² = (x4 + 1) / x²

 

Gruß asinus :- )

laugh!

 Feb 13, 2016
edited by asinus  Feb 13, 2016
 #3
avatar+105604 
0

x+1/x=25   x^2+1/x^2=?

 

\(x+\frac{1}{x}=25\qquad \qquad x^2+\frac{1}{x^2}=?\\~\\ (x+\frac{1}{x})^2=25^2\\ x^2+\frac{1}{x^2}+2=625\\ x^2+\frac{1}{x^2}=623\\ \)

.
 Feb 13, 2016

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