In this page quadratic equation practical solution1 we are going to see solution of practice question of the worksheet quadratic equation practical application.
Question 1:
The sum of a number and its reciprocal is 65/8. Find the number
Solution:
Let “x” be the required number, then “1/x” will be its reciprocal
Sum of a number and its reciprocal is 65/8
x + (1/x) = 65/8
(x² + 1)/x = 65/8
8 (x² + 1) = 65 x
8 x² + 8 - 65 x = 0
8 x² - 65 x + 8 = 0
8 x² – 1 x - 64 x + 8 = 0
x (8 x - 1) – 8 (8 x – 1) = 0
(x – 8) = 0 (8x – 1) = 0
x – 8 = 0 8 x – 1 = 0
x = 8 8 x = 1
x = 1/8
Therefore the two required numbers are 8 and 1/8
Verification:
Sum of the number and its reciprocal is 65/8
= 8 + (1/8)
= (64 + 1)/8
= 65/8
Therefore the answer what we got is correct.
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