Fun question to solve:
Assume that $x_1, x_2, ..., x_7$ 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
$$16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7$$
and no, it's not 1234.

Question

Fun question to solve:
Assume that $x_1, x_2, ..., x_7$ 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
$$16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7$$
and no, it's not 1234.

lgbasallote · Answer

lol you and your fun..why cant it be sports =_=

anonymous · Answer

Its always fun when Linear Algebra is involved. It turns out that:$$16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7= $$$$(x_1+4x_2+9x_3+16x_4+25x_5+36x_6+49x_7)$$$$-3(4x_1+9x_2+16x_3+25x_4+36x_5+49x_6+64x_7)$$$$+3(9x_1+16x_2+25x_3+36x_4+49x_5+64x_6+81x_7)$$This gives us:$$1-3(12)+3(123)=334$$