Maths Olympiad Prep

Track / Stage 2 / 138 of 320 #458 of 2604

Problem 458

Algebra Difficulty 2.2 Find the answer CEMC Fermat

What is the value of (5abla1)+(4abla1)(5 abla 1)+(4 abla 1) if the operation kablamk abla m is defined as k(k−m)k(k-m)?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Next problem →

Official solution

From the definition, (5abla1)+(4abla1)=5(5−1)+4(4−1)=5(4)+4(3)=20+12=32(5 abla 1)+(4 abla 1)=5(5-1)+4(4-1)=5(4)+4(3)=20+12=32.

Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.