If-a-b-c-are-3-positive-numbers-in-an-A-P-and-T-a-8b-2b-a-8b-c-2b-c-Then-the-value-of-T-2-is-Ans-given-is-361-

Question Number 32532 by rahul 19 last updated on 28/Mar/18

I f a, b, c a r e 3 p o s i t i v e n u m b e r s i n a n

A . P a n d

T = \frac{a + 8 b}{2 b - a} + \frac{8 b + c}{2 b - c} .

T h e n t h e v a l u e o f T^{2} i s ?

A n s . g i v e n i s 361 .

Commented by Rasheed.Sindhi last updated on 28/Mar/18

b = a + d, c = a + 2 d

T = \frac{a + 8 b}{2 b - a} + \frac{8 b + c}{2 b - c}

= \frac{a + 8 (a + d)}{2 (a + d) - a} + \frac{8 (a + d) + (a + 2 d)}{2 (a + d) - (a + 2 d)}

= \frac{9 a + 8 d}{a + 2 d} + \frac{9 a + 10 d}{a}

= \frac{9 a^{2} + 8 a d + 9 a^{2} + 10 a d + 18 a d + 20 d^{2}}{a (a + 2 d)}

= \frac{18 a^{2} + 36 a d + 20 d^{2}}{a (a + 2 d)}

= \frac{2 (9 a^{2} + 18 a d + 10 d^{2})}{a (a + 2 d)}

T {can}^{'} t be free of a & d

Also T is even (Its square should also even)

∴ T^{2} \neq 361

Commented by Tinkutara last updated on 28/Mar/18

W h e n (a, b, c) = (3, 5, 7)

T = \frac{43}{7} + \frac{47}{3}

T^{2} \neq 361

Commented by rahul 19 last updated on 28/Mar/18

O k, t h a n k y o u b o t h!