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If x2−y2=x+yx^{2}-y^{2}=x+y, then x−y=x-y=

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Csc, sec, and cot of special anglesright chevron icon

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Q. If x2−y2=x+yx^{2}-y^{2}=x+y, then x−y=x-y=
  1. Recognize as difference of squares: Recognize the equation x2−y2=x+yx^2 - y^2 = x + y as a difference of squares.\newlinex2−y2=(x+y)(x−y)x^2 - y^2 = (x + y)(x - y)
  2. Set equation: Set the equation (x+y)(x−y)=x+y(x + y)(x - y) = x + y.\newlineSince x+y≠0x + y \neq 0 (otherwise x2−y2=0x^2 - y^2 = 0, which doesn't match the original equation unless both xx and yy are zero), we can divide both sides by x+yx + y.\newlinex−y=1x - y = 1

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