x and y
Find the value of x + y so that it satisfies both equations:
x 2 0 1 7 + y 2 0 1 8 = 1 y 2 0 1 7 + x 2 0 1 8 = 1
The answer is 8070.
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2 solutions
x 2 0 1 7 + y 2 0 1 8 = 1 x y 2 0 1 7 y + 2 0 1 8 x = 1 2 0 1 7 y + 2 0 1 8 x = x y . . . ( 1
y 2 0 1 7 + x 2 0 1 8 = 1 x y 2 0 1 7 x + 2 0 1 8 y = 1 2 0 1 7 x + 2 0 1 8 y = x y . . . ( 2
Thus it is found that equation ( 1 equals the equation ( 2 .
2 0 1 7 y + 2 0 1 8 x = 2 0 1 7 x + 2 0 1 8 y x = y
Substitute
2 0 1 7 x + 2 0 1 8 y = x y 2 0 1 7 x + 2 0 1 8 x = x 2 4 0 3 5 x = x 2 4 0 3 5 = x 4 0 3 5 = y
So, x + y = 4 0 3 5 + 4 0 3 5 = 8 0 7 0
2017/x + 2018/y = 1 (eq1)
2017/y + 2018/x = 1 (eq2)
(eq2) -(eq1)
=1/x - 1/y = 0
Therefore, x = y
(eq1) equals 2017/x+ 2018/x = 1
Therefore, x = 4035
Therefore, x+y = 2(x) = 8070