Question

1. The sum of a number and its reciprocal is 65\8 . Find the number

Answer 1

Take the number as x
sum of a number and its reciprocal is 65/8 so we have
x+1/x=65/8
8x^2+8=65x
8x^2-65x+8=0
8x^2-64x-x+8=0
8x(x-8)-1(x-8)=0
(8x-1)(x-8)=0
x=8,1/8
So the numbers are 8 or 1/8

Answer 2

solution :

Let the number = x

reciprocal of the number = 1/x

x + 1/x = 65/8 ( given )

⇒ ( x² + 1 )/x = 65/8

⇒ 8( x² + 1 ) = 65x

⇒ 8x² + 8 - 65x = 0

⇒ 8x² - 65x + 8 = 0

⇒ 8x² - 64x - 1x + 8 = 0

⇒ 8x( x - 8 ) -1( x - 8 )= 0

⇒ ( x - 8 )( 8x - 1 ) = 0

∴ x -8 = 0 or 8x - 1 = 0

x = 8 or x = 1/8

∴ required number = x = 8

Or

x = 1/8

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