If p²− 4p − 1 = 0, then the value of p²+ 3p + 1/(p²) - 3/p is:

If p²− 4p − 1 = 0, then the value of p²+ 3p + 1/(p²) - 3/p…

If p²− 4p − 1 = 0, then the value of p²+ 3p + $\frac{1}{p^2} - \frac{3}{p}$ is:

Show answer & explanation

Correct answer: D

Explanation

The correct answer is option 4 i.e. 30.

p² − 4p − 1 = 0 ⇒ p² = 4p + 1 और 1/p² = 1/(4p + 1)

Expression:

p² + 3p + 1/p² − 3/p

= (4p + 1) + 3p + 1/(4p + 1) − 3/p

= 7p + 1 + 1/(4p + 1) − 3/p

Let p = 2 + √5 (root of given equation)

Then:

7p = 14 + 7√5

3/p = −6 + 3√5

1/(4p + 1) = 9 − 4√5

Add:

7p + 1 + 1/(4p + 1) − 3/p

= (14 + 7√5) + 1 + (9 − 4√5) − (−6 + 3√5)

= 21 + 4√5 + (9 − 4√5) = 30