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Integer Root (Tomato Subjective 43)

Show that the equation \(x^3 + 7x – 14(n^2 +1) = 0 \) has no integral root for any integer n.

Solution:

We note that \(14(n^2 +1) – 7x = x^3 \) implies \(x^3 \) is divisible by 7. This implies x is divisible by 7 (as 7 is a prime number). Suppose x= 7x’. Hence we can rewrite the given equation as:

\(7^3 x’^3 + 7 \times 7 x’ – 14 (n^2 +1 ) = 0 \).

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1 comment

  1. ISI B. Math solved questions needed

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