Solve this problem from the work of Antonio de'Mazzinghi. Find two numbers such that multiplying one...

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Solve this problem from the work of Antonio de'Mazzinghi. Find two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27. (Put the first number equal to x + and the second equal to x — j; then the two equations are x2 — y = 8 and 2x2 + 2y = 27.
	
Document Preview: Solve this problem from the work of Antonio de’Mazzinghi.  Find two numbers such 
that multiplying one by the other makes 8 and the sum of their squares is 27.  (Put the 
first number equal to     and the second equal to    ; then the two equations 
v v
  
are       and         .

Robert · Accepted Answer

Let the first number be A=  x+ sqrt(y) 
And second number be B = x –sqrt(y) 
given conditions 
AB = 8  
Or x2 – y =8 ..(i) 
And A^2 +B^2 = 27  
Or 2x2 + 2y =27--- (ii) 
(ii) – 2*(i) gives 
4y = 11 
Or y = 11/4 =2.75 ; 
Putting this value in eqn (i) we get 
X2 = 10.75 
Or x=  ±3.

Solve this problem from the work of Antonio de'Mazzinghi. Find two numbers such that multiplying one by the other makes 8 and the sum of their squares is 27. (Put the first number equal to x + and the...

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