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Find all values of y that satisfy the equation y/3 + 1 = (y + 3)/y + 7.

 Feb 14, 2022
 #1
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To make the equation clear, it looks like this: \({y\over3}+1={y+3\over y}+7\).

Then multiply every term by '3y'.

 

It should now look like this:\(y^2 + 3y = 3y + 9 + 21y\).

Combining like terms and moving the equation to one side, we get: \(y^2 - 21y - 9 = 0\).

 

Then you can use the quadratic formula \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\) where a is the coefficient of x^2. b is the coefficient of x, and c is the constant.

Plugging in the values, we have:

 

\(y = {21 + 3\sqrt{53}\over2}\)

\(y = {21-3\sqrt{53}\over2}\)

 

Those are the two possible values of y :)

 Feb 14, 2022

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