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hemang (1665)

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x^2 - 19x + 94 = (x - 19/2)^2 + 15/4 = m^2

(2x - 19)^2 + 15 = 4m^2.

-15 = (2x - 19 - 2m)(2x - 19 + 2m)

15 = (19 + 2m - 2x)(2x - 19 + 2m).

15 = 15*1 = 3*5 = -3*-5 = -15*-1.

no we can equate this.

19 + 2m - 2x = 1. and 2x - 19 + 2m = 15.

x - m = 9. and x + m = 17.

so, at x = 13, m = 4.

similarly all solutions are =

m = + 4, - 4 , x = 13

m = +4, -4, x = 6.

m = +2, -2, x = 10.

m = +2, -2, x = 9.

the answer is 13...

:)


mathematics is the food of my soul. There are 3 types of people in the world. Those who can count and those who can't . :-)
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