We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
123
2
avatar

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

 Aug 1, 2019
 #1
avatar+19832 
+2

By looking at it    x = 4

 

5+4   *   20-4

9      *    16      =  144

 Aug 1, 2019
 #2
avatar+23342 
+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

2 Online Users