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14 Jul 2026, 10:11
Kudos
Bookmarks
Given a^2 - b^2 = 945
(a-b)(a+b) = 945
Let x = a - b and y = a + b
Then, xy = 945
Since 945 is odd, both x and y must be odd, so each factor pair gives a unique integer pair (a, b).
Prime Factor of 945 = 3^3 * 5 * 7
No of Factors: (3+1)(1+1)(1+1) = 16
Since, xy > 0, both factors must have the same sign:
-> 16 +ve ordered pairs
-> 16 -ve ordered pairs
Total = 32 ordered pairs
Answer: (D) 32
(a-b)(a+b) = 945
Let x = a - b and y = a + b
Then, xy = 945
Since 945 is odd, both x and y must be odd, so each factor pair gives a unique integer pair (a, b).
Prime Factor of 945 = 3^3 * 5 * 7
No of Factors: (3+1)(1+1)(1+1) = 16
Since, xy > 0, both factors must have the same sign:
-> 16 +ve ordered pairs
-> 16 -ve ordered pairs
Total = 32 ordered pairs
Answer: (D) 32
14 Jul 2026, 10:18
Kudos
Bookmarks
a and b are integers i.e. they could be -ve, 0, + ve
Ordered pair means (a,b) and (b,a) are different pairs.
945 = a^2-b^2 =(a-b)*(a+b) = 5*3^3*7
There are total (1+1)*(3+1)*(1+1) =16 number of factors of this number 945. (e.g. (1,945), (5,189), (15,63) etc.)
(a-b) and (a+b) could be +ve or -ve. Hence, for both negative numbers, there are other 16 factors.
Thus, there are total 32 number of ordered pairs.
Answer = D
Ordered pair means (a,b) and (b,a) are different pairs.
945 = a^2-b^2 =(a-b)*(a+b) = 5*3^3*7
There are total (1+1)*(3+1)*(1+1) =16 number of factors of this number 945. (e.g. (1,945), (5,189), (15,63) etc.)
(a-b) and (a+b) could be +ve or -ve. Hence, for both negative numbers, there are other 16 factors.
Thus, there are total 32 number of ordered pairs.
Answer = D
Bunuel
14 Jul 2026, 10:27
Kudos
Bookmarks
a^2 - b^2 = 945
(a-b) (a+b) = 945
since 945 is an odd number (a-b) and (a+b) must both be odd.
Factor 945 = 5 x 189 = 5 x 9 x 21 = 5^1 x 3^3 x 7^1
Number of positive divisors you add one to the factors and multiple
(3+1) (1+1) (1+1) = 4 x 2 x 2 = 16
Since (a + b) and (a - b) can also both be negative then 16 x 2 = 32
Answer D 32
(a-b) (a+b) = 945
since 945 is an odd number (a-b) and (a+b) must both be odd.
Factor 945 = 5 x 189 = 5 x 9 x 21 = 5^1 x 3^3 x 7^1
Number of positive divisors you add one to the factors and multiple
(3+1) (1+1) (1+1) = 4 x 2 x 2 = 16
Since (a + b) and (a - b) can also both be negative then 16 x 2 = 32
Answer D 32
