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If ?^?– ?? − ? = ? has rational roots then find the minimum value of c, where c is a natural number.

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28 COMMENTS

  1. Minimum value of c is 8. The discriminant 49 + 4c must be = some perfect square = y^2 (say), otherwise the roots won't be rational. So c should be (y^2 – 49)/4, which should be >=1 since c is a natural no. –> y^2 >= 53 –> y^2 =81 gives c as lowest possible natural no. which is 8 (for y^2 = 64, c comes out as 15/4, a fraction).

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