System of equations?
Let and be distinct numbers satisfying the system of equations above.
What is the value of ?
The answer is 15.
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1 solution
expanding y + 4 = ( x − 2 ) 2 and x + 4 = ( y − 2 ) 2
we get y = x 2 − 4 x and x = y 2 − 4 y
x − y = ( y − 2 ) 2 − ( x − 2 ) 2
Difference of squares
x − y = [ ( y − 2 ) − ( x − 2 ) ] ∗ [ ( y − 2 ) 2 + ( x − 2 ) 2 ]
x − y = ( y − x ) ∗ ( y + x − 4 )
x − y = ( − 1 ) ∗ ( x − y ) ∗ ( y + x − 4 )
( x − y ) / [ ( − 1 ) ∗ ( x − y ) ] = ( y + x − 4 )
− 1 = y + x − 4
x + y = 3
then
y + x = x 2 − 4 x + y 2 − 4 y
x 2 + y 2 = 5 x + 5 y
x 2 + y 2 = 5 ∗ ( x + y )
x 2 + y 2 = 5 ∗ ( 3 )
x 2 + y 2 = 1 5