MathGrit
ProblemsTechniquesPricing
Sign inGet started
Back to problems

AIME 1989 #8 — Seven Reals Power Sums System

2525MasterSystems Of EquationsAlgebra

AIME · 1989 · Problem 8

Assume that $x_1,x_2,\ldots,x_7$ are real numbers such that $$\begin{align*} x_1 + 4x_2 + 9x_3 + 16x_4 + 25x_5 + 36x_6 + 49x_7 &= 1, \\ 4x_1 + 9x_2 + 16x_3 + 25x_4 + 36x_5 + 49x_6 + 64x_7 &= 12, \\ 9x_1 + 16x_2 + 25x_3 + 36x_4 + 49x_5 + 64x_6 + 81x_7 &= 123. \end{align*}$$ Find the value of $16x_1+25x_2+36x_3+49x_4+64x_5+81x_6+100x_7$.
0 students attempted0% solvedRating 2525

Related practice paths

AIME PracticeInteger-answer practice for deeper multi-step problems.How to Qualify for AIMEScore goals, contest choice, and prep habits for AIME hopefuls.How to Review Missed AMC ProblemsTurn missed problems into a repeatable improvement loop.

Ready to check your answer?

Create an account to submit answers, save history, and track your rating.

Progressive Hints5

Unlock hints one at a time — each reveals a little more without spoiling the solution.

Step-by-Step Solutions1

Multiple solution approaches with detailed walkthroughs, unlocked after you solve the problem.

AI-Powered Grading

Instant feedback on your answer — handles fractions, decimals, and equivalent forms.

Curated problem bank

Supported tracks for AMC, AIME, MATHCOUNTS, and olympiad-style training, plus global problem sources like UKMT, Euclid, and Kangaroo.