Evaluate $\frac{a^4}{(a-b)(a-c)}+\frac{b^4}{(b-c)(b-a)}+\frac{c^4}{(c-a)(c-b)}$ Let $$a=-\sqrt{99}+\sqrt{999}+\sqrt{9999}$$
$$b = \sqrt{99}-\sqrt{999}+\sqrt{9999}$$
$$c = \sqrt{99}+\sqrt{999}-\sqrt{9999}$$
Evaluate $$\frac{a^4}{(a-b)(a-c)}+\frac{b^4}{(b-c)(b-a)}+\frac{c^4}{(c-a)(c-b)}$$
Edited work :
$$\frac{a^4(b-c) + b^4(c-a)+c^4(a-b)}{(a-b)(a-c)(b-c)}$$
$$\frac{(a-b)(a-c)(b-c)(a^2+b^2+c^2+ab+ac+bc)}{(a-b)(a-c)(b-c)}$$
$$a^2+b^2+c^2+ab+ac+bc$$
$$a(a+b) +b(b+c) +c(c+a)$$
Ans : $$2(99+999+9999)=22194$$

HINT: simplifying at first and you will get $${a}^{2}+ba+ac+{b}^{2}+bc+{c}^{2} $$ and now you can plug in the given values
