Evaluate the symmetric expression.

01 / Standard#Your turn

x^2-3x+1=0,\quad x^4+x^{-4}=?

Official paper · jm01-2024 · I.14 · PDF 3

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Divide by x; x is nonzero.

Hint 2

Square twice and subtract the cross term each time.

Worked solution

B: 47.

Checks and common pitfalls: The product x²·x⁻² is 1, so the cross term is 2.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Find x²+x⁻².
$x+x^{-1}=3\implies x^2+x^{-2}=9-2=7$
Square again.
$x^4+x^{-4}=7^2-2=47$

Think first. Reveal a hint when the class is ready.

2024 JM01