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    Question

    If {x + (1/x)} = 7, then find the value of

    {x2┬а- (1/x)2}.
    A 21тИЪ7 Correct Answer Incorrect Answer
    B 32тИЪ7 Correct Answer Incorrect Answer
    C 42тИЪ5 Correct Answer Incorrect Answer
    D 21тИЪ5 Correct Answer Incorrect Answer

    Solution

    Given = {x + (1/x)} = 7 On, squaring both sides, we have; {x + (1/x)}2┬а= 72 Or, x2┬а+ (1/x)2┬а+ 2 = 49 Or, {x2┬а+ (1/x)2} = 47 On subtracting '2' from both sides, we have; {x2┬а+ (1/x)2┬а- 2} = 45 Or, {x - (1/x)}2┬а= 45 So, {x - (1/x)} = 3тИЪ5 Since, (a2┬а- b2)┬а= (a + b) X (a - b) {x2┬а- (1/x)2}┬а= {x - (1/x)}┬аX {x + (1/x)} = 3тИЪ5 X 7 = 21тИЪ5

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