24QOD repeated here
If x can be any real number, then find the value of
\frac{(x-a)(x-b)(x-c)}{(d-a)(d-b)(d-c)}+\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)} - 1
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3 Answers
23consider the question to be f(x)
f(x) is a polynomial of degree three
now for x=a,b,c,d
i.e for 4 values of x
f(x) = 0
hence f(x)= 0 is an identity , and is true for all x
