A) 3
B) 4
C) 5
D) 6
Correct Answer: B
Solution :
[b] \[{{a}^{2}}-{{b}^{2}}=512\Rightarrow (a+b)(a-b)={{2}^{9}}\] \[\Rightarrow (a+b,a-b)=({{2}^{8}},2),({{2}^{7}},{{2}^{2}}),({{2}^{6}},{{2}^{3}}),({{2}^{5}},{{2}^{4}})\] Since \[a>b,a+b>a-b\] therefore the other combinations like \[({{2}^{4}},{{2}^{5}})\] etc. cannot be accepted \[({{2}^{9}},1)\] also cannot be accepted since a and b are positive integers.
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