The impossible equation
If ⎩ ⎪ ⎪ ⎨ ⎪ ⎪ ⎧ x = 2008 repeated 2018 times 2 0 0 8 2 0 0 8 2 0 0 8 2 0 0 8 2 0 0 8 . . . 2 0 0 8 2 0 0 8 y = 2007 repeated 2018 times 2 0 0 7 2 0 0 7 2 0 0 7 2 0 0 7 2 0 0 7 . . . 2 0 0 7 2 0 0 7 then find the value of 2 0 0 7 x − 2 0 0 8 y .
The answer is 0.
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3 solutions
x = 2 0 0 8 ( 1 0 2 0 1 8 + 1 0 2 0 1 7 + 1 0 2 0 1 6 + ⋯ + 1 0 0 )
y = 2 0 0 7 ( 1 0 2 0 1 8 + 1 0 2 0 1 7 + 1 0 2 0 1 6 + ⋯ + 1 0 0 )
Let's assign the letter P to 1 0 2 0 1 8 + 1 0 2 0 1 7 + 1 0 2 0 1 6 + ⋯ + 1 0 0
Therefore, x = 2 0 0 8 P and y = 2 0 0 7 P
2 0 0 7 x − 2 0 0 8 y = 2 0 0 7 × 2 0 0 8 P − 2 0 0 8 × 2 0 0 7 P
= 0 .
Fantastic metbod
x=2008(1+10^4+10^8+.... to 2018 terms) Therefore x=2008((10^4)^2018 -1)÷(10^4-1) Similarly y=2007*((10^4)^2018-1)÷(10^4-1) So we get, 2007x=2008y Therefore ans=0
Mast kiya bhai
x = 2008 repeated 2018 times 2 0 0 8 2 0 0 8 2 0 0 8 . . . 2 0 0 8 = 2 0 1 8 ( 0001 repeated 2018 times 1 0 0 0 1 0 0 0 1 . . . 0 0 0 1 ) = 2 0 1 8 a , where a = 0001 repeated 2018 times 1 0 0 0 1 0 0 0 1 . . . 0 0 0 1 ) . Similarly, y = 2 0 0 7 a . Then 2 0 0 7 x − 2 0 0 8 y = 2 0 0 7 ( 2 0 0 8 a ) − 2 0 0 8 ( 2 0 0 7 a ) = 0 .