Question

6(p-1/p)=5,find the value of p^2+1/p^2=?​

Answer 1

Answer :

97/36

Solution :

• Given : 6(p - 1/p) = 5
• To find : p² + 1/p² = ?

We have ;

=> 6(p - 1/p) = 5

=> p - 1/p = 5/6

Now ,

Squaring both the sides , we get ;

=> (p - 1/p)² = (5/6)²

=> p² + (1/p)² - 2•p•(1/p) = 25/36

=> p² + 1/p² - 2 = 25/36

=> p² + 1/p² = 25/36 + 2

=> p² + 1/p² = (25 + 72)/36

=> p² + 1/p² = 97/36

Hence ,

p² + 1/p² = 97/36

Answer 2

$\large{\underline{\underline{\rm{\maltese\:\: \red{Question \: : }}}}}$

If 6(p - $\frac{1}{p}$) = 5 , find the value of $P^2 + \frac{1}{p^2}$ = ?

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$\large{\underline{\underline{\rm{\maltese\:\: \red{Answer \: : } }}}}$

$\boxed{\bold{p^2 + \frac{1}{p^2} = \frac{97}{36}}}$

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$\large{\underline{\underline{\rm{\maltese\:\: \red{Given\: : } }}}}$

• 6(p - $\frac{1}{p}$) = 5

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$\large{\underline{\underline{\rm{\maltese\:\: \red{To\: Find \: : } }}}}$

• $P^2 + \frac{1}{p^2}$ = ?

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$\large{\underline{\underline{\rm{\maltese\:\: \red{Concept \: Used: } }}}}$

• (a + b)² = a² + b² + 2ab

• (a - b)² = a² + b² - 2ab

• (a + b) (a - b) = a² - b²

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$\large{\underline{\underline{\rm{\maltese\:\: \red{Solution \: : } }}}}$

$6(p - \frac{1}{p}) = 5$

$\implies p - \frac{1}{p} = \frac{5}{6}$

Now , Squaring both LHS as well as RHS. We get,

$(p - \frac{1}{p})^2= (\frac{5}{6})^2$

$\implies p^2 + \frac{1}{p^2} - (2\:*\not{p}*\frac{1}{\not{p}}) = \frac{25}{36}$

$\implies p^2 + \frac{1}{p^2} - 2 = \frac{25}{36}$

$\implies p^2 + \frac{1}{p^2} = \frac{25}{36} + 2$

$\implies p^2 + \frac{1}{p^2} = \frac{25 \: +\: (36*2)}{36}$

$\implies p^2 + \frac{1}{p^2} = \frac{25 \: + 72}{36}$

$\implies p^2 + \frac{1}{p^2} = \frac{97}{36}$

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$\large{\underline{\underline{\rm{\maltese\:\: \red{Answer \: : } }}}}$

$\boxed{\bold{p^2 + \frac{1}{p^2} = \frac{97}{36}}}$

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