Given-that-a-number-is-a-factor-of-144-and-the-square-of-the-number-added-to-five-times-the-number-is-6-find-the-number-

Question Number 35425 by Rio Mike last updated on 18/May/18

G i v e n t h a t a n u m b e r i s a f a c t o r

o f 144 a n d t h e s q u a r e o f t h e n u m b e r

a d d e d t o f i v e t i m e s t h e n u m b e r

i s ⩾ - 6 f i n d t h e n u m b e r

Answered by Rasheed.Sindhi last updated on 19/May/18

n ∣ 144 \land n^{2} + 5 n ⩾ - 6

n^{2} + 5 n + 6 ⩾ 0

(n + 2) (n + 3) ⩾ 0

(n + 2) (n + 3) = 0 ∣^{*} (n + 2) (n + 3) > 0

n = - 2 ∣ n = - 3 \dots \dots \dots I

^{*} (n + 2) (n + 3) > 0

n + 2 > 0 \land n + 3 > 0 ∣ n + 2 < 0 \land n + 3 < 0

n > - 2 \land n > - 3 ∣ n < - 2 \land n < - 3

n > - 2 ∣ n < - 3 \dots \dots \dots . . II

I & II : n ⩾ - 2 or n ⩽ - 3

Hence

Factors of 144 ⩾ - 2 or ⩽ - 3

{, . . - 8 - 6, - 4, - 3, - 2, - 1, 1, 2, 3, 4, 6, 8 \dots .}

= {\pm 1, \pm 2, \pm 3, \pm 4, \pm 6, \pm 8, \pm 9, \dots .}

Or All the factors of 144