Question : If $p^{2} - 4 p - 1 = 0$ , then the value of $p^{2} + 3 p + \frac{1}{p^{2}} - \frac{3}{p}$ is:
Option 1: 40
Option 2: 50
Option 3: 65
Option 4: 30

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Question : If $\sec A = \frac{9}{4}$ , then what is the value of $\cot A$ ?

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Answer 1

Correct Answer: 30

Solution : Given: $p^{2} - 4 p - 1 = 0$
⇒ $p - \frac{1}{p} = 4$
Squaring both sides, we get:
$\Rightarrow (p - \frac{1}{p})^{2} = (4)^{2}$
$\Rightarrow (p^{2} + \frac{1}{p^{2}} - 2 \times p \times \frac{1}{p}) = 16$
$\Rightarrow (p^{2} + \frac{1}{p^{2}}) = 16 + 2$
$\Rightarrow (p^{2} + \frac{1}{p^{2}}) = 18$
Now, $p^{2} + 3 p + \frac{1}{p^{2}} - \frac{3}{p}$
$= p^{2} + \frac{1}{p^{2}} + 3 p - \frac{3}{p}$
$= p^{2} + \frac{1}{p^{2}} + 3 (p - \frac{1}{p})$
Putting the values, we get:
$= 18 + 3 \times 4$
$= 30$
Hence, the correct answer is 30.

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Question : If p2−4p−1=0, then the value of p2+3p+1p2−3p is:Option 1: 40Option 2: 50Option 3: 65Option 4: 30

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Question : If $p^{2} - 4 p - 1 = 0$ , then the value of $p^{2} + 3 p + \frac{1}{p^{2}} - \frac{3}{p}$ is:
Option 1: 40
Option 2: 50
Option 3: 65
Option 4: 30