Tricky problem

Submitted by humraj on Thu, 2007-11-01 15:46

Let M = (10⁴ + 324)(22⁴ + 324)(34⁴ + 324)(46⁴ + 324)(58⁴ + 324)

and N = (4⁴ + 324)(16⁴ + 324)(28⁴ + 324)(40⁴ + 324)(52⁴ + 324).

What is the value of M/N?

Posted on: Thu, 2007-11-15 21:14 #1

Joined: 2007-08-24

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HUMRAJ!!!!!!!!

Sol.

We know a⁴+ 4b⁴= (a²+ 2b²- 2ab)(a²+ 2b²+ 2ab)

M = (10⁴ + 324)(22⁴ + 324)(34⁴ + 324)(46⁴ + 324)(58⁴ + 324)

M = (100 + 18 - 60)(100 + 18 + 60)(484 + 18 - 132)(484+18+132) ..... (3364 + 18 - 348)(3364 + 18 + 348)

M = (58)(178)(370)(634).........(3034)(3730)

N = (4⁴ + 324)(16⁴ + 324)(28⁴ + 324)(40⁴ + 324)(52⁴ + 324)

N = (16 + 18 - 24)(16 + 18 + 24)(256 + 18 - 96)(256 + 18 + 96)........(2704 + 18 - 312)(2704 + 18 + 312)

N = (10)(58)(178)(370)...........(2410)(3034)

M/N = 373

Posted on: Fri, 2007-11-16 02:11 #2

Joined: 2007-03-03

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Thanks

it was just tooooooooo tricky

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