Difference between revisions of "1989 AIME Problems/Problem 8"

 
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== Problem ==
 
== Problem ==
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Assume that <math>x_1,x_2,\ldots,x_7</math> are real numbers such that
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<center><math>x_1+4x_2+9x_3+16x_4+25x_5+36x_6+49x_7=1^{}_{}</math></center>
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<center><math>4x_1+9x_2+16x_3+25x_4+36x_5+49x_6+64x_7=12^{}_{}</math></center>
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<center><math>9x_1+16x_2+25x_3+36x_4+49x_5+64x_6+81x_7=123^{}_{}</math></center>
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Find the value of <math>16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7^{}</math>.
  
 
== Solution ==
 
== Solution ==
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{{solution}}
  
 
== See also ==
 
== See also ==
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* [[1989 AIME Problems/Problem 9|Next Problem]]
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* [[1989 AIME Problems/Problem 7|Previous Problem]]
 
* [[1989 AIME Problems]]
 
* [[1989 AIME Problems]]

Revision as of 22:06, 24 February 2007

Problem

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 $16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7^{}$.

Solution

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See also

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