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Proof by mathematical induction

Prove that pr...

Question

Prove that product of two consecutive natural number cannot be $441$ .

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Solution

$l e t t h e n a t u r a l n u m b e r b e n t h e n n (n + 1) = 441 n^{2} + n - 441 = 0 D = b^{2} - 4 a c = 1^{2} - 4 \times 1 \times (- 441) = 1 + 4 \times 441 = 1 + (42)^{2} ∴ \sqrt{} D w i l l n o t b e a n i n t e g e r a n d h e n c e n = (\frac{- b \pm \sqrt{} D}{2 a}) w i l l n o t b e a n i n t e g e r, s o w e c a n c o n c l u d e p r o d u c t o f t w o c o n s e c u t i v e n u m b e r c a n n o t b e 441$

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