| x + 1/x | > or = 2 (Question: 232453.0 )

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SIDDHARTHSHANKAR

· started a discussion

· 1 Months ago

| x + 1/x | > or = 2 (Question: 232453.0 )

Respected admin;

Here (x + 1/x) = 5/2 & 3/2 after solving quadratic equation. How can expression (x + 1/x) be less than 2 for any value of x???

So in my opinion it should be 5/2 ...

Please correct me in case I am wrong .....

Question:

If $(x^{2} + \frac{1}{x^{2}})$ − 4 $(x + \frac{1}{x})$ + $\frac{23}{4}$ = 0. Find $(x + \frac{1}{x}) .$

Options:

5/2

3/2

Both (a) and (b)

None of these

Solution:

Ans: (c) $(x^{2} + \frac{1}{x^{2}})$ − 4 $(x + \frac{1}{x})$ + $\frac{23}{4}$ = 0

$(x^{2} + \frac{1}{x^{2}} + 2)$ − 4 $(x + \frac{1}{x})$ + $\frac{23}{4}$ − 2= 0

${(x + \frac{1}{x})}^{2}$ − 4 $(x + \frac{1}{x})$ + $\frac{15}{4}$ = 0

Let $(x + \frac{1}{x})$ = k

K² – 4k + $\frac{15}{4}$ = 0

4K² – 16k + 15 = 0

(2k – 5)(2k – 3) = 0

K = 5/2, 3/2

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Knowledge Expert

· commented

· 1 Months ago

Dear Student,
No where in the question given that x is an integer, it also can be fraction, So go through the answer marked.
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