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Find the sum of all numbers x satisfying x+25/x = 10.

 Apr 21, 2019
 #1
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I'm assuming that the question is asking to find the answer to (x + 25)/x = 10

To find the answer you must first multiply both sides by x to remove the denominator of x in the fraction, leaving you with x + 25 = 10x

Next, subtract x from both sides in order to get all your x's on the same side: 25 = 9x

Lastly, just divide both sides by 9 to remove the coefficient of x, leaving you with an answer of x = 25/9 or 2 7/9

 Apr 21, 2019
 #2
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NO!, that is NOT right:

 

x+25/x = 10                              Put the LHS over the common denominator x

[x^2 + 25] / x = 10                    Cross multiply

x^2 + 25 = 10x                         Subtract 10x from both sides

x^2 - 10x + 25 =0                     Write the LHS as a square

(x - 5)^2 = 0                             Take the square of both sides

x - 5 = 0                                    Add 5 to both sides

x = 5 - Both roots are the same

x = 5

Sum = 5 + 5 =10

 Apr 21, 2019
edited by Guest  Apr 21, 2019
 #3
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It was x+(25/x)=10 sorry :(

 Apr 21, 2019
 #4
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\(x^2 + 25 = 10x\)

\(x^2 -10x + 25 = 0\)

By the quadratic formula,

\(\boxed{x=5}\)

This is the only solution, so the answer is \(5\) as well.

.
 Apr 21, 2019
edited by Guest  Apr 21, 2019

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