Assume that \(x_1,x_2,\ldots,x_7\) are real numbers such that $$x_1+4x_2+9x_3+16x_4+25x_5+36x_6+49x_7=1^{}_{}$$ $$4x_1+9x_2+16x_3+25x_4+36x_5+49x_6+64x_7=12^{}_{}$$ $$9x_1+16x_2+25x_3+36x_4+49x_5+64x_6+81x_7=123^{}_{}$$ Find the value of \(16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7^{}\).

(第七届AIME1989 第8题)