If the number of integral solutions x , y , z of the equation x y z = 18 is t , then the value of t 8 is

Question

If the number of integral solutions x , y , z of the equation x y z = 18 is t , then the value of t 8 is,

MARKS App · Accepted Answer

18 = 1.1 . 18 = 1.2 . 9 = 1.3 . 6 = 2.3 . 3 Each of 1,2 , 9 , 1,3 , 6 can be permuted in 3 ! ways Each of 1,1 , 18 , 2,3 , 3 can be permuted in 3 ways So, there are 2 × 3 ! + 2 × 3 = 18 triplets x , y , z Also, the signs are + , – , – , – , + , – , – , – , + , + , + , + , So, the desired number is 18 × 4 = 72 Hence, 72 8 = 9

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