# Quintic Expression

Algebra Level pending

Let a,b,c and d be distinct real numbers such that

$$a$$ + $$b$$ +$$c$$ + $$d$$ = 3 and
$$a^2$$ + $$b^2$$ + $$c^2$$ + $$d^2$$ =45

Then Find the value of $\frac{a^5}{(a-b)(a-c)(a-d)}+\frac{b^5}{(b-a)(b-c)(b-d)}+\frac{c^5}{(c-a)(c-b)(c-d)}+\frac{d^5}{(d-a)(d-b)(d-c)}$

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