Difference between revisions of "1989 AIME Problems/Problem 8"
m |
|||
Line 1: | Line 1: | ||
== Problem == | == Problem == | ||
+ | Assume that <math>x_1,x_2,\ldots,x_7</math> are real numbers such that | ||
+ | <center><math>x_1+4x_2+9x_3+16x_4+25x_5+36x_6+49x_7=1^{}_{}</math></center> | ||
+ | <center><math>4x_1+9x_2+16x_3+25x_4+36x_5+49x_6+64x_7=12^{}_{}</math></center> | ||
+ | <center><math>9x_1+16x_2+25x_3+36x_4+49x_5+64x_6+81x_7=123^{}_{}</math></center> | ||
+ | |||
+ | Find the value of <math>16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7^{}</math>. | ||
== Solution == | == Solution == | ||
+ | {{solution}} | ||
== See also == | == See also == | ||
+ | * [[1989 AIME Problems/Problem 9|Next Problem]] | ||
+ | * [[1989 AIME Problems/Problem 7|Previous Problem]] | ||
* [[1989 AIME Problems]] | * [[1989 AIME Problems]] |
Revision as of 23:06, 24 February 2007
Problem
Assume that are real numbers such that
![$x_1+4x_2+9x_3+16x_4+25x_5+36x_6+49x_7=1^{}_{}$](http://latex.artofproblemsolving.com/8/1/8/818dab4381c68ad6ddc6950e9c6d22ba7ee9e7aa.png)
![$4x_1+9x_2+16x_3+25x_4+36x_5+49x_6+64x_7=12^{}_{}$](http://latex.artofproblemsolving.com/7/4/a/74a188f2fd92f4adb96ca93685391e9e5fcb0b3b.png)
![$9x_1+16x_2+25x_3+36x_4+49x_5+64x_6+81x_7=123^{}_{}$](http://latex.artofproblemsolving.com/2/c/f/2cf66ae792a08e91ace7eaafee395079e1d0231b.png)
Find the value of .
Solution
This problem needs a solution. If you have a solution for it, please help us out by adding it.