The sum of two numbers is 11 and the sum of their reciprocals is 1128 Find the numbers.
Given sum of two numbers is 11
x+y=11 _____ (1)
sum of their reciprocals is 1128.
1x+1y=1148
y+xxy=1148
28(x+y)=11xy _______ (2)
28(11)=11.xy
xy=28
Now
(x−y)2=x2+y2−2xy
(x−y)2=(x+y)2−4xy
(x−y)2=(11)2−4×28
(x−y)2=121−112
(x−y)2=9
x−y=√9
x−y=3 _______ (3)
On adding (1) & (3)
x+y=1
x−y=3
_________
2x=14
x=142
x=7
putting x=7 in equation _____ (1)
x+y=11
7+y=11
y=11−7
y=4
∴ The two numbers are (x,y)=(7,4)