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Question

The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the sum of squares of the numbers.

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Solution

Let one number be x, then other number will be 9x
According to the question,
1x+19x=12
9x+xx(9x)=12
99xx2=12
2(9)=9xx2
18=9xx2
x29x+18=0
x26x3x+18=0
x(x6)3(x6)=0$
(x6)(x3)=0
x6=0 and x3=0
x=6 and x=3
One number is 6 and other number is 3
The sum of squares of the numbers =(6)2+(3)2=36+9=45

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