AMU Engineering 2017 solved paper Solved Paper

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