Question
Download Solution PDFIf x2 - 7x + 1 = 0, and 0 < x < 1, what is the value of x2 -
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula Used :
x + (1/x) = a
Then x - (1/x) = √(a2 - 4)
Calculation :
⇒ x2 - 7x + 1 = 0
On dividing by x we get :
⇒ x - 7 + (1/x) = 0
⇒ x + (1/x) = 7
Now, (x - 1/x) = -√(49 - 4) = - √45 = - 3√5
[Here 0 < x < 1 so x - (1/x) < 0]
⇒ x2 - (1/x2) = [x - (1/x)] [x + (1/x)]
⇒ 7 × (-3√5)
⇒ -21√5
∴ The correct answer is - 21√5.
Mistake Points
Here 0 < x < 1
⇒ 1/x > 1
⇒ x - 1/x < 0
Thus, x2 - (1/x2) = [x - (1/x)] [x + (1/x)] < 0
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