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If sqrt{5 + x} + sqrt{20 - x} = 7, what is the value of (5 + x)(20 - x)?

 Aug 1, 2019
 #1
avatar+19908 
0

By looking at it    x = 4

 

5+4   *   20-4

9      *    16      =  144

 Aug 1, 2019
 #2
avatar+23850 
+2

If \(\sqrt{5 + x} + \sqrt{20 - x} = 7\), what is the value of \((5 + x)(20 - x)\)?

 

\(\begin{array}{|rcll|} \hline \sqrt{5 + x} + \sqrt{20 - x} &=& 7 \quad &|\quad \text{square both sides} \\ \left(\sqrt{5 + x} + \sqrt{20 - x}\right)^2 &=& 7^2 \\ \left(\sqrt{5 + x}\right)^2 +2\sqrt{5 + x} \sqrt{20 - x} + \left(\sqrt{20 - x}\right)^2 &=& 49 \\ 25 +2\sqrt{(5 + x)(20 - x)} &=& 49 \quad &|\quad -25 \\ 2\sqrt{(5 + x)(20 - x)} &=& 49-25 \\ 2\sqrt{(5 + x)(20 - x)} &=& 24 \quad &|\quad : 2 \\ \sqrt{(5 + x)(20 - x)} &=& 12 \quad &|\quad \text{square both sides} \\ \left( \sqrt{(5 + x)(20 - x)}\right)^2 &=& 12^2 \\ \mathbf{(5 + x)(20 - x)} &=& \mathbf{144} \\ \hline \end{array}\)

 

laugh

 Aug 1, 2019

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