Question

How many pairs of integers (a, b) are possible
such that a^2-b^2 = 288 ?​

Answer 1

Answer:

288=1×288

288=2×144

288=4×72

288=8×36

288=16×18

288=32×9

288=96×3

So ,a^2-b^2=288

(a+b)(a-b)=288

2×144=288

a+b=144 a-b =2

Adding both equations

2a=146

a=73 b=71

Similarly others values can be found

These are as follows

(a,b)=(38,34) (22,14) (17,1) (73,71)

Values with 32×9, 96×3, 288×1 are not possible as integer values are not coming