Question
If {x + (1/x)} = 7, then find the value of
{x2 - (1/x)2}.Solution
Given = {x + (1/x)} = 7 On, squaring both sides, we have; {x + (1/x)}2 = 72 Or, x2 + (1/x)2 + 2 = 49 Or, {x2 + (1/x)2} = 47 On subtracting '2' from both sides, we have; {x2 + (1/x)2 - 2} = 45 Or, {x - (1/x)}2 = 45 So, {x - (1/x)} = 3√5 Since, (a2 - b2) = (a + b) X (a - b) {x2 - (1/x)2} = {x - (1/x)} X {x + (1/x)} = 3√5 X 7 = 21√5
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