sum of a positive number and its reciprocal is 65/8. Find the number
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Let the positive number be x
ATQ
x + 1/x = 65 /8
⇒ (x² + 1) / x = 65/8
⇒ x² + 1 = 65x / 8
⇒ 8x² + 8 = 65x
⇒ 8x² - 65x + 8= 0
⇒ 8x² - 64x - x + 8= 0
⇒ 8x ( x - 8) -1 ( x - 8) = 0
⇒ (8x -1) ( x - 8) = 0
So x can be 1/8 or 8
Note that 1/8 and 8 both are positive numbers, if you've asked for a natural number then your answer will be 8.
ATQ
x + 1/x = 65 /8
⇒ (x² + 1) / x = 65/8
⇒ x² + 1 = 65x / 8
⇒ 8x² + 8 = 65x
⇒ 8x² - 65x + 8= 0
⇒ 8x² - 64x - x + 8= 0
⇒ 8x ( x - 8) -1 ( x - 8) = 0
⇒ (8x -1) ( x - 8) = 0
So x can be 1/8 or 8
Note that 1/8 and 8 both are positive numbers, if you've asked for a natural number then your answer will be 8.
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