UKMT - Senior Mathematical Challenge - 2022 - 19 | Exact Science

19

How many pairs of real numbers (x, y) satisfy the simultaneous equations x² - y = 2022 and y² - x = 2022?

A. infinitely many B. 1 C. 2 D. 3 E. 4

Answer

E

SOLUTIOn

The two parabolas described by the equations intersect at four points, leading to four real solutions for the system.

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Curriculum Mathematics

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Curriculum Mathematics

Our goal at this course is to enhance our students’ mathematical intuition by focusing on a deep understanding of mathematical concepts and to enable them to link different concepts and apply their knowledge to solve mathematical problems to help them to improve their performance at Maths exams.

Olympiad Mathematics

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Olympiad Mathematics

Olympiad Mathematics is a comprehensive course designed to help students win UKMT competitions. It is suitable for high-achieving mathematics students who are looking to take their skills to the next level.

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Introduction to Python with Turtle

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Coding in Python

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Olympiad Geometry

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Prepare for the Primary Maths Challenge

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