. The sum of a number and its reciprocal is 10/3. Find the number.

*CLUE* multiply both sides by “x” to begin

Guest Nov 26, 2018

#1**+1 **

Solve for x:

x + 1/x = 10/3

Bring x + 1/x together using the common denominator x:

(x^2 + 1)/x = 10/3

Cross multiply:

3 (x^2 + 1) = 10 x

Expand out terms of the left hand side:

3 x^2 + 3 = 10 x

3x^2 - 10x + 3 = 0

Use the quadratic formula to solve for x:

**x = 3 or x = 1/3**

Guest Nov 27, 2018

edited by
Guest
Nov 27, 2018

#1**+1 **

Best Answer

Solve for x:

x + 1/x = 10/3

Bring x + 1/x together using the common denominator x:

(x^2 + 1)/x = 10/3

Cross multiply:

3 (x^2 + 1) = 10 x

Expand out terms of the left hand side:

3 x^2 + 3 = 10 x

3x^2 - 10x + 3 = 0

Use the quadratic formula to solve for x:

**x = 3 or x = 1/3**

Guest Nov 27, 2018

edited by
Guest
Nov 27, 2018

#2**+1 **

Taking the Guest's answer from here :

3x^2 - 10x + 3 = 0

We can use a factoring "trick" to solve this.....write - 10x as -9x - x

3x^2 - 9x - x + 3 = 0 factorby grouping

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

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

Setting both factor to 0 and solving for x produces

x = 3 or x = 1/3

CPhill Nov 27, 2018