Question

if a2+1/a2 = 23 find the value of a+1/a

Answer 1

Answer:

5

Step-by-step explanation:

(a+1/a)^2 = a^2+1/a^2 + 2 . a.1/a

(a+1/a)^2= 23+2

(a+1/a)^2= 25

(a+1/a)= root 25

(a+1/a) = 5

hope this will help you

pls mark me a brainlist

Answer 2

Answer

• The value of $\bold{a + \cfrac{1}{a } = 5}$

Given

• The value of $\sf {a}^{2} + \cfrac{1}{ {a}^{2} } = 23$

To Find

• The value of $\sf a + \cfrac{1}{a}$

Step By Step Explanation

In this question we have given the value of $\sf {a}^{2} + \cfrac{1}{ {a}^{2} } = 23$.

We need to find the value of $\sf a + \cfrac{1}{a}$

So let's do it !!

Identity Used :

$\bigstar \: \: \: \: \underline{\boxed{ \bold{ \purple{{(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy}}}}$

By substituting the values :

$:\implies{\sf{ \bigg(a + \cfrac{1}{a} \bigg) }^{2} = {a}^{2} + \cfrac{1}{ {a}^{2} } + \bigg(2 \times a \times \cfrac{1}{a} \bigg)} \\ \\ :\implies{\sf{ \bigg(a + \cfrac{1}{a} \bigg) }^{2} = {a}^{2} + \cfrac{1}{ {a}^{2} } + \bigg(2 \times \cancel{a} \times \cfrac{1}{ \cancel{a}} \bigg)} \\ \\ :\implies{\sf{ \bigg(a + \cfrac{1}{a} \bigg) }^{2} = {a}^{2} + \cfrac{1}{ {a}^{2} } + 2} \\ \\ :\implies{\sf{ \bigg(a + \cfrac{1}{a} \bigg) }^{2} = ( 23) + 2} \\ \\:\implies {\sf{ \bigg(a + \cfrac{1}{a} \bigg) }^{2} = 25} \\ \\:\implies {\sf{a + \cfrac{1}{a} } = \sqrt{25}} \\ \\ :\implies \underline{\boxed{\bold{\green{a + \cfrac{1}{a} = 5}}}} \: \: \: \: \dag$

Therefore, the value of $\bold{a + \cfrac{1}{a } = 5}$

__________________________