Solution for
Lim (x+y)²/x²+y²=?
Answers
Answer:
25
Step-by-step explanation:
(x-y)^2=25 >>>x-y=+-5
and x^2+y^2=73 >>x^2+y^2+2xy=73+2*24=73+48=121
=(x+y)^2=121>>>x+y=+-sqrt 121=+-11 and
x-y=+-5>>>x=(+-11 (+) +-5)/2 and after finding x we can compute y!!!
Another way is : x-y=-+5>>x=y+-5 replace in x^2+y^2=73
(y+-5)^2+y^2=73 we get 2 quadratc equations in y with 4 y solutions and then replace x in x-y=+-5 we get x=y-+5 !! 4 solutions
Shortly:x=8, y=3!!!Also x=-8, y=-3 and x=3 , y=8 and x=-3 y=-8!!!
Resuming: (x-y)^2=25 .The system HAS at 4 (FOUR) SOLUTIONS, it is SYMMETRIC, it means replacing x with y doesn’t change anything…, if a symmetric system has solution x=a and y=b then the system has also the resolution x=b, y=a!
The person putting this equation thinks only of positive numbers actually this is a DIOFANTIC EQUATION having also negative solutions, integers. If we want to FIND all solutions we shall exhaust the definition domain satisfying the requirements…
So: (x-y)^2=25, but above I gave ALL SOLUTION….a)x=8, y=3, b)x=-8, y=-3 ,c) x=3 , y=8 and d) x=-3 y=-8. The solutions verify the system.
Q.E.D
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