Question

The sum of a number and it's reciprocal is 10/3.Find the number ​

Answer 1

Let the number be x and 1/x,

Then, x + 1/x = 10/3

⇒ (x2 + 1)/x = 10/3

⇒ 3x2 - 10x + 3 = 0

⇒ 3x2 - 9x - x + 3 = 0

⇒ 3x(x - 3) -1 (x - 3) = 0

⇒ (3x - 1) (x - 3) = 0

∴ x = 1/3, x = 3

Answer 2

Answer:

Let the number be x and 1/x

=> x + 1/x = 10/3

=> (x2 + 1)/x = 10/3

=> 3( x2 + 1 ) = 10x

=> 3x2 + 3 = 10x

=> 3x2 - 10x + 3 = 0

=> 3x2 - x - 9x + 3 = 0

=> x(3x - 1) - 3 (3x - 1) = 0

=> (3x - 1) (x - 3) = 0

=> 3x - 1 = 0 , x - 3 = 0

=> 3x = 1 , x = 3

=> x = 1/3

Hence, x = 1/3, 3 Ans.

Step-by-step explanation:

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