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If sqrt(x) + sqrt(y) = 13 and 4x + 9y = 793, what is the value of x?

 Jul 27, 2022
 #1
avatar+2270 
+1

Let \(\sqrt{x} = m\) and let \( \sqrt{y}=n\)

 

We now have a new system: 

 

\(4m^2 + 9n^2 = 793 \ \ \ \ \ \ \ \ (i)\)

\(m + n = 13 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ (ii)\)

 

From \((ii)\), we have \(n = 13 - m \).

 

Plugging this into \((i)\) gives us \(4m^2 + 9(13 - m)^2 = 793\), which simplifies to \(13m^2 + 1521 - 234m=793\).

 

Subtracting \(793\) from both sides gives us \(13m^2 - 234m + 728 = 0\).

 

Now, solve for \(m\), square it, and plug it into both equations to make sure it works.

 

Good luck!

 Jul 27, 2022
 #2
avatar+2270 
+1

This was my 1000th answer lol...

 Jul 27, 2022

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