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Simplifying f2 + g2 = 2fg Solving f2 + g2 = 2fg Solving for variable 'f'. Reorder the terms: -2fg + f2 + g2 = 2fg + -2fg Combine like terms: 2fg + -2fg = 0 -2fg + f2 + g2 = 0 Factor a trinomial. (f + -1g)(f + -1g) = 0Subproblem 1
Set the factor '(f + -1g)' equal to zero and attempt to solve: Simplifying f + -1g = 0 Solving f + -1g = 0 Move all terms containing f to the left, all other terms to the right. Add 'g' to each side of the equation. f + -1g + g = 0 + g Combine like terms: -1g + g = 0 f + 0 = 0 + g f = 0 + g Remove the zero: f = g Simplifying f = gSubproblem 2
Set the factor '(f + -1g)' equal to zero and attempt to solve: Simplifying f + -1g = 0 Solving f + -1g = 0 Move all terms containing f to the left, all other terms to the right. Add 'g' to each side of the equation. f + -1g + g = 0 + g Combine like terms: -1g + g = 0 f + 0 = 0 + g f = 0 + g Remove the zero: f = g Simplifying f = gSolution
f = {g, g}
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