Question

if p2-3p+1=0 and find p2+1/p2​

Answer 1

p² - 3p + 1 = 0

_____________ [GIVEN]

• We have to find the value of p² + $\dfrac{1}{ {p}^{2} }$

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Solution:

$\implies$ p² - 3p + 1 = 0

$\implies$ p² + 1 = 3p

Divide by p on both sides

$\implies$ $\dfrac{ {p}^{2} }{p}$ + $\dfrac{1}{p}$ = $\dfrac{3p}{p}$

$\implies$ p + $\dfrac{1}{p}$ = 3

Now.. squaring on both sides..

$\implies$ $\bigg ({p \: + \: \dfrac{1}{p}} \bigg)^{2}$ = (3)²

• (a + b)² = a² + b² + 2ab

$\implies$ $\bigg ( {p}^{2} \: + \: \dfrac{1}{ {p}^{2} } \: + \: 2p \: \times \: \dfrac{1}{p} \bigg)$ = 9

$\implies$ p² + $\dfrac{1}{ {p}^{2} }$ + 2 = 9

$\implies$ p² + $\dfrac{1}{ {p}^{2} }$ = 9 - 7

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$\huge{\bold{{p}{^2}\:+\:\dfrac{1}{p}^{2} \: =\:7}}$

_____________ $\bold{[ANSWER]}$

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Answer 2

Answer:

hope it helps you.....