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Find all ordered pairs x, y of real numbers such that x+y=10 and x^2+y^2=64.
For example, to enter the solutions (2, 4) and (-3, 9), you would enter "(2,4),(-3,9)" (without the quotation marks).

 Jun 19, 2024
 #1
avatar+129725 
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x + y = 10    →   y  = 10 - x

 

x^2  + (10-x)^2 = 64

 

2x^2 - 20x + 100 = 64

 

2x^2 -20x + 36 =  0

 

x^2 -10x + 18  =  0 

 

x^2 - 10x  =   -18

 

x^2 -10x + 25  = -18 + 25

 

(x - 5)^2  = 7            take both roots

 

x - 5 = sqrt 7            or            x  - 5 = -sqrt 7

 

x = 5 + sqrt 7                          x  = 5 - sqrt 7

 

(x , y)  = (5 + sqrt 7 , 5 -sqrt 7 )   or ( 5 -sqrt 7 , 5 + sqrt 7)

 

 

cool cool cool

 Jun 20, 2024

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