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Explanation
The sum of a number and its reciprocal is one eighth of 34.
The product of the number and its square root will be figure out in this way.
Let suppose the number is y.
One-eighth of 34
34 x 1/8
The sum of y and 1/y
y + 1/y = 34 x 1/8 ________ (i)
Through equation (i) we can easily find out the value of y (y = 4).
By multiplying the value of “y” with its “square root” we can easily figure out the product as is done in solution.
To Find
Number = ?
Solution
Let suppose
Number = y
According to the given condition
y + 1/y = 34 x 1/8
8(y2 + 1) = 34y
8y2 + 8 = 34y
8y2 – 34y + 8 = 0
4y2 – 17y + 4 = 0
4y2 – 16y – 1y + 4 = 0
4y(y – 4) – 1(y – 4) = 0
(4y – 1)(y – 4) = 0
4y – 1 = 0 & y – 4 = 0
y = 1/4 & y = 4
It means the number is “4”.
The product of the number and its square root
Required Product = 4 x 2 = 8 answer
Conclusion
The sum of a number and its reciprocal is one eighth of 34. The product of the number and its square root is 8.
