Let two number be a and b; (a>b) According to the question, a−b=12 ........(i) and
a+b
2
−√ab=2 ⇒a+b−2√ab=4 ........(ii) ⇒a+b=4+2√ab ⇒(a+b)2=(4+2√ab)2 [Squaring both sides ] ⇒(a−b)2+4ab=16+4ab+16√ab‌‌[∵(x+y)2=(x−y)2+4xy] ⇒(12)2=16+16√ab‌‌‌[ from Eq. (i)] ⇒√ab=8 On substituting √ab=8 in Eq. (ii), we get a+b−16=4 or a+b=20........ (iii) On solving Eqs. (i) and (iii), we get a=16,b=4