MathDB

8

Part of 1989 AIME Problems

Problems(1)

Perfect Square Sequence

Source:

2/20/2006
Assume that x1,x2,…,x7x_1,x_2,\ldots,x_7 are real numbers such that x1+4x2+9x3+16x4+25x5+36x6+49x7=1        4x1+9x2+16x3+25x4+36x5+49x6+64x7=12     9x1+16x2+25x3+36x4+49x5+64x6+81x7=123. \begin{array}{r} 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. \\ \end{array} Find the value of 16x1+25x2+36x3+49x4+64x5+81x6+100x7.16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7.
algebrapolynomialfunctionquadraticsAMCAIMErational function