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# need help

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

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

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

Nov 27, 2018
edited by Guest  Nov 27, 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
#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   Nov 27, 2018