AP EAMCET · Maths · Quadratic Equation
The number of integral solutions of \(2\left(x^2+\frac{1}{x^2}\right)-7\left(x+\frac{1}{x}\right)+9=0\) when \(x \neq 0\) is
- A 1
- B 2
- C 4
- D 0
Answer & Solution
Correct Answer
(A) 1
Step-by-step Solution
Detailed explanation
Let \(y = x + \frac{1}{x}\). \(2(y^2-2)-7y+9=0 \Rightarrow 2y^2-7y+5=0\) \(y = \frac{7 \pm \sqrt{49-40}}{4} = \frac{7 \pm 3}{4}\) \(y = \frac{5}{2}\) or \(y = 1\) If \(x + \frac{1}{x} = \frac{5}{2} \Rightarrow 2x^2-5x+2=0 \Rightarrow (2x-1)(x-2)=0 \Rightarrow x=2\) (integral) or…
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