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# system

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

Jul 27, 2022

#1
+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
+2270
+1

This was my 1000th answer lol...

Jul 27, 2022