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avatar+193 

Let $a\star b = \dfrac{\sqrt{a+b}}{\sqrt{a-b}}$. If $ x \star 24 = 7$, find $x$.

 Feb 5, 2021
 #1
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x must be 25 since sqrt(25+24) = sqrt(49) = 7, and sqrt(25-24) = sqrt(1) =1.

 Feb 6, 2021
 #2
avatar+113120 
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I am not familiar with this notation.

 Feb 6, 2021
 #3
avatar+32110 
+3

This is just defining the operator *.

You replace a by x, b by 24 and the result by 7 so:

 

Alan  Feb 6, 2021
 #4
avatar+113120 
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Thanks Alan

Melody  Feb 6, 2021
 #5
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note that 7-24-25 is a pythagorean triple

 Feb 6, 2021

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