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If p2 + 1/p2 = 83, then the numerical value of p - 1/p will be
- A9
- B7/4
- C± 6
- D3
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CCommunity
Consider the given equation,
p2 + 1/p2 = 83
Subtract 2 from both sides of the equation.
$( \Rightarrow {p^2} + \frac{1}{{{p^2}}} - 2 = 81)$
$( \Rightarrow {p^2} + \frac{1}{{{p^2}}} - 2 \times {p^2} \times \frac{1}{{{p^2}}} = 81)$
$( \Rightarrow {\left( {p - \;\frac{1}{p}} \right)^2} = 81)$
⇒ (p - 1/p) = √81
⇒ (p - 1/p) = ±9
As, only +9 is given in the options, option A is the answer.
p2 + 1/p2 = 83
Subtract 2 from both sides of the equation.
$( \Rightarrow {p^2} + \frac{1}{{{p^2}}} - 2 = 81)$
$( \Rightarrow {p^2} + \frac{1}{{{p^2}}} - 2 \times {p^2} \times \frac{1}{{{p^2}}} = 81)$
$( \Rightarrow {\left( {p - \;\frac{1}{p}} \right)^2} = 81)$
⇒ (p - 1/p) = √81
⇒ (p - 1/p) = ±9
As, only +9 is given in the options, option A is the answer.