IIT JEE , AIEEE Forum - Mathematics , Algebra - no of solutions.........find plz.........

blackjack

the number of positive integral solutions of the equation x1x2x3x4x5=1050 is_______???

plz giv detailed soln

sboosy

I suppose everybody is very serious about VITEEE because the same question has come thrice in 3 days

Here is the link

http://www.goiit.com/posts/list/algebra-the-number-of-positive-integral-solutions-of-the-equation-53706.htm

rtiit

1050=2.3.5.5.7

the answer is 1875.....

consider a,b,c,d,e as five boxes(x1,x2,x3,x4,x5)

2,3,7 can enter these boxes in 5*5*5 ways

5 can enter these boxes as two 5's or one 25
so no of ways = 5C1+5C2=15 ways

toatl no of ways = 5*5*5*15=1875 ways

so total no of solutions is 1875

little_genius

let me give the solution for any given no ....it wud be helpful....

let n= x1x2x3.x4x5= 2^a,3^b,5^c.....

then x1 = 2^@1.3^@2.5^@3.........
similarly for x2,x3,x4....

now we have @1 +%1 +.....= a total no of integral soln will give the answer........

this is a very long method but i tried it myself ...others may give shorter ways....

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