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CBSE Class 10 Answered

The fourth power of the common difference of an arithmetic progression with integer entries added to the product of any four consecutive terms of it . Prove that the resulting sum is the square of an integer
Asked by rushabhjain.a | 20 Feb, 2019, 09:05: PM
answered-by-expert Expert Answer
Let four consecutive terms of an A. P. are a - 3d, a - d, a + d, a + 3dwhich are integers.
According to the question, 
(a - 3d)(a - d)(a + d)(a + 3d) + (2d)4
Solving we get
(a - 3d)(a + 3d) + (2d)2 which is an integer.
(a - 3d)(a - d)(a + d)(a + 3d) + (2d)4 = I2
Answered by Sneha shidid | 21 Feb, 2019, 10:09: AM

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