Challenging +1.8 This question requires geometric insight (recognizing that |x+y| + |x-y| = 2 describes a square with vertices at (±1,0) and (0,±1)), then optimizing x² - 6x + y² = (x-3)² + y² - 9 over this region. It combines modulus inequalities, geometric interpretation, and optimization—significantly harder than routine A-level questions but accessible to strong Further Maths students.
3. If for some \(x , y \in \mathbb { R }\) we have \(| x + y | + | x - y | = 2\), find the maximal value of \(x ^ { 2 } - 6 x + y ^ { 2 }\). [0pt]
[Question 3 - Continued] [0pt]
[Question 3 - Continued] [0pt]
[Question 3 - Continued]
3. If for some $x , y \in \mathbb { R }$ we have $| x + y | + | x - y | = 2$, find the maximal value of $x ^ { 2 } - 6 x + y ^ { 2 }$.\\[0pt]
[Question 3 - Continued]\\[0pt]
[Question 3 - Continued]\\[0pt]
[Question 3 - Continued]\\
\hfill \mbox{\textit{SPS SPS FM 2022 Q3 [20]}}