If p+1/p=12,find the value of p-1/p - Maths - Algebraic Expressions and Identities

Question

If p+1/p=12,find the value of p-1/p

ramandeep.singh · Accepted Answer

$p + \frac{1}{p} = 12$

On squaring both sides, we get

$p^{2} + 2 (p) (\frac{1}{p}) + \frac{1}{p^{2}} = 144 \Rightarrow p^{2} + 2 + \frac{1}{p^{2}} = 144$

On subtracting 4 from both sides, we get

$p^{2} + 2 + \frac{1}{p^{2}} - 4 = 144 - 4 \Rightarrow p^{2} - 2 + \frac{1}{p^{2}} = 140 \Rightarrow p^{2} - 2 (p) (\frac{1}{p}) + \frac{1}{p^{2}} = 140 \Rightarrow (p - \frac{1}{p})^{2} = 140 ∴ (p - \frac{1}{p}) = \pm \sqrt{140} = \pm 2 \sqrt{35}$