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x2+(x+y)2=9x^{2}+(x+y)^{2}=9

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Full solution

Q. x2+(x+y)2=9x^{2}+(x+y)^{2}=9
  1. Expand and Simplify Equation: First, let's expand the equation to simplify it.\newlineWe have x2+(x+y)2=9x^2 + (x + y)^2 = 9.\newlineExpanding (x+y)2(x + y)^2 gives us x2+2xy+y2x^2 + 2xy + y^2.\newlineSo the equation becomes x2+x2+2xy+y2=9x^2 + x^2 + 2xy + y^2 = 9.
  2. Combine Like Terms and Simplify: Now, let's combine like terms. We have 2x2+2xy+y2=92x^2 + 2xy + y^2 = 9. To simplify, we can divide the entire equation by 22 to make it easier to work with. This gives us x2+xy+y22=92x^2 + xy + \frac{y^2}{2} = \frac{9}{2}.

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