. The sum of a number and its reciprocal is 10/3. Find the number.
*CLUE* multiply both sides by “x” to begin
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
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
+130536 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
