#1723 · Algebra · Polynomials

Conditions for a Bivariate Quadratic Square

Prove that $a x^{2} + 2 b x y + c y^{2} + 2 d x + 2 ey + f$ is a perfect square, if $b^{2} = a c$ , $d^{2} = a f$ , $e^{2} = c f$ .

~15 minProof · checked by AIundetermined coefficientspolynomialsidentities

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXII. Undetermined Coefficients, Examples XXII.a, No. 9

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