Question

How many pairs of natural numbers is there the difference of whose squares are 45.
A.1
B.2
C.3
D.4

Answer 1

i think 4 if 4 is wrong then 3

Answer 2

Answer:

3 Pairs

Step-by-step explanation:

($a^{2} - b^{2}$) = 45

we know, ($a^{2} - b^{2}$) = (a+b)(a-b)

(a+b)(a-b) = 45

Now, the factors of 45 are 1 x 45, 3 x 15, 9 x 5.

get values for both a & b by considering the above values of each bracket.

Eg. (a+b) = 9 and (a-b) = 5 solving this we get a = 7 and b = 2. Do the same process for the rest.

Thus we get the possible values of a and be to be 9 & 6 or 7 & 2 or 23 & 22. Hence there are 3 pairs that satisfy the condition given in the question.