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OlympiadBench / 2317 / If T=x²+(1)/(x²), determine the values of b and c so that…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

If T=x2+1x2T=x^{2}+\frac{1}{x^{2}}, determine the values of bb and cc so that x6+1x6=T3+bT+cx^{6}+\frac{1}{x^{6}}=T^{3}+b T+c for all non-zero real numbers xx.
Plain-text mathematical notation (without MathML)
If T=x²+(1)/(x²), determine the values of b and c so that x⁶+(1)/(x⁶)=T³+bT+c for all non-zero real numbers x.
Original LaTeX notation
If $T=x^{2}+\frac{1}{x^{2}}$, determine the values of $b$ and $c$ so that $x^{6}+\frac{1}{x^{6}}=T^{3}+b T+c$ for all non-zero real numbers $x$.

answer type

Numerical

is multiple answer

true

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID
2317
task_id
7877c3c3-cd1d-5435-af28-ecf4ed376a04
task_key
OE~5fTO~5fmaths~5fen~5fCOMP--train--2317
task_revision_id
4
config / split
OE_TO_maths_en_COMP / train

Official source

initial import