When 2(a + b)(c + d)(a*c + b*d – x) is the square of an integer

 
 
The integers   a, b, c, d,   and   x   are such that

a^2 \; + \; x \; = \; b^2
c^2 \; + \; x \; = \; d^2
 
Show that   2 \,(a + b) \,(c + d) \,(a \, c + b \, d - x)   is the square of an integer
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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