#1886 · Algebra · Polynomials

Lagrange Interpolation Identity Cubic

Prove the identity: $\frac{( x - b ) ( x - c ) ( x - d )}{( a - b ) ( a - c ) ( a - d )} + \frac{( x - c ) ( x - d ) ( x - a )}{( b - c ) ( b - d ) ( b - a )} + \frac{( x - d ) ( x - a ) ( x - b )}{( c - d ) ( c - a ) ( c - b )} + \frac{( x - a ) ( x - b ) ( x - c )}{( d - a ) ( d - b ) ( d - c )} = 1$ .

~15 minProof · checked by AIundetermined coefficientsidentitiespartial fractions

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. XXII. Undetermined Coefficients, Examples XXII.a, No. 12 (part 2)

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