Question

✨50 points✨

Q)X+1/x=13/6,5/6 and 4/3

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Answer 1

SOLUTION

1st CASE

x + (1/x) = 13/6 (multipy both sides by x  )

x^2 + 1 = 13x/6(multiply both sides by 6  )

6x^2 + 6 = 13x (subtract 13x from both sides  )

6x^2 - 13x + 6 = 0 (factor the quadratic)

(2x-3) * (3x-2) = 0  

2x - 3 = 0 or 3x - 2 = 0  

x = 3/2 or x = 2/3  

check by substituting

x + 1/x = 13/6  

3/2 + 2/3 = 13/6  

9/6 + 4/6 = 13/6  

13/6 = 13/6  

2/3 + 3/2 = 13/6  

4 + 9 = 13  

13 = 13

2nd Case

→x+ (1/x) = 5/6 (multipy both sides by x  )

→x^2 + 1 = 5x/6(multiply both sides by 6  )

→6x^2 + 6 = 5x (subtract 5x from both sides  )

→6x^2 - 5x -6 = 0 (factor the quadratic)

→6x(x-9)+4(x-9)=0

→(x-9) (6x+4)=0

→x - 9= 0 or 6x +4 = 0  

→x = 9 or x =-2/3

Answer 2

Refer to the attachment!!