4MA1/1HR Jan 2022, Question 15: Expand and Simplify
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 3 marks
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The question, in short
Using algebra, show that for any 3 consecutive whole numbers, the squares of the smallest and largest add to 2 more than twice the middle square.
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Solution · 3 marks
- 1Let the numbers be n, n + 1 and n + 2
- 2Smallest² + largest² = n² + (n + 2)² = 2n² + 4n + 4
- 3Twice the middle² = 2(n + 1)² = 2n² + 4n + 2
- 42n² + 4n + 4 = (2n² + 4n + 2) + 2, so the sum is always 2 more
AnswerWith n, n + 1, n + 2: n² + (n + 2)² = 2n² + 4n + 4 and 2(n + 1)² = 2n² + 4n + 2, so the sum is 2 more
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