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: solve for x,y {[(x-y)^(2)+4=3y-5x+2sqrt()(x+1)(y-1)],[(3xy-5y+6x+11)/(sqrt(x^(3)+1))=5]:}

solve for x,yx,y\newline{[(x−y)2+4=3y−5x+2(x+1)(y−1)],[3xy−5y+6x+11x3+1=5]}\left\{\left[(x-y)^{2}+4=3y-5x+2\sqrt{(x+1)(y-1)}\right],\left[\frac{3xy-5y+6x+11}{\sqrt{x^{3}+1}}=5\right]\right\}

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Q. solve for x,yx,y\newline{[(x−y)2+4=3y−5x+2(x+1)(y−1)],[3xy−5y+6x+11x3+1=5]}\left\{\left[(x-y)^{2}+4=3y-5x+2\sqrt{(x+1)(y-1)}\right],\left[\frac{3xy-5y+6x+11}{\sqrt{x^{3}+1}}=5\right]\right\}
  1. Analyze and Simplify: Step 11: Analyze and simplify the first equation.\newlineEquation: (x−y)2+4=3y−5x+2(x+1)(y−1)(x-y)^2 + 4 = 3y - 5x + 2\sqrt{(x+1)(y-1)}\newlineRewrite without the square root for simplicity:\newline(x−y)2+4=3y−5x+2(x+1)(y−1)(x-y)^2 + 4 = 3y - 5x + 2\sqrt{(x+1)(y-1)}
  2. Isolate Terms: Step 22: Attempt to isolate terms in the first equation.\newlineExpand (x−y)2(x-y)^2:\newlinex2−2xy+y2+4=3y−5x+2(x+1)(y−1)x^2 - 2xy + y^2 + 4 = 3y - 5x + 2\sqrt{(x+1)(y-1)}
  3. Simplify Second Equation: Step 33: Analyze and simplify the second equation.\newlineEquation: (3xy−5y+6x+11)/x3+1=5(3xy - 5y + 6x + 11) / \sqrt{x^3 + 1} = 5\newlineMultiply both sides by x3+1\sqrt{x^3 + 1} to clear the denominator:\newline3xy−5y+6x+11=5x3+13xy - 5y + 6x + 11 = 5\sqrt{x^3 + 1}
  4. Solve Using Methods: Step 44: Attempt to solve the system using substitution or elimination.\newlineThis step involves complex algebraic manipulation or numerical methods, which might be challenging without specific values or further simplification.

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