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airsealands
30.08.2020 •
Mathematics
Solve the two following simultaneous equations and find the possible values of x and y.
![x^2 - y^2 = 40](/tpl/images/1733/5606/6ab85.png)
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Ответ:
Step-by-step explanation:
(*) x^2 + y^2 - 2xy = 64
<=> (x - y)^2 = 64
<=> x - y = 8 or x - y = -8
(**) x^2 - y^2 = 40
<=> (x - y)(x + y) = 40
Case 1: x - y = 8
(**) <=> 8(x + y) = 40
<=> x + y = 5
we have: x+y = 5 and x-y = 8
--> x = (5+8)/2 = 6.5
--> y = x - 8 = 6.5 - 8 = -1.5
so (x,y) = (6.5 , -1.5)
Case 2: x - y = -8
(**) <=> -8(x + y) = 40
<=> x + y = -5
we have: x + y = -5 and x - y = -8
--> x = [ (-5) + (-8) ]/2 = -6.5
--> y = -5 - x = -5 + 6.5 = 1.5
so (x,y) = (-6.5 , 1.5)
(x,y) = (6.5 , -1.5) and (-6.5 , 1.5)
Ответ:
68
Step-by-step explanation: