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Find the value of x & y

Find the value of x & y. We have only one equation: 16x.x+y + 16x+y.y = 1(16 to the power x.x + y + 16 to the power x+y.y = 1.

I have found that X =-1/2 & y = -1/2 satisfying this equation. But I got it through trial method. It will be helpful, if anyone can solve this.

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