Question

obtain the triangular number upto 60 how many e are there

Answer 1

Step-by-step explanation:

Let the numbers be x and y then x

2

−y

2

=60 ⇒(1)

or (x−y)(x+y)=60 ⇒(2)

Factors of 60:

5×12

2×30

4×15

1×60

3×20

6×10

We go for even pairs (2,30) and (6,10)

since even−odd pair wont satisfy condition(2)

checking even pairs in condition(1)

x−y=2, x+y=30 →x=16,y=14

& x−y=6, x+y=10 →x=8, y=2

Hence, only 2 sets of Natural numbers