Question

If a^2 + 1/a^2 =18 then find : a-1/a

Answer 1

given
a^2+1/a^2=18
then.! ,
(a-1/a)^2+2=18
=>(a-1/a)^2=16
=>(a-1/a)=4

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Answer 2

Answer:

$a-\frac{1}{a}=\pm 4$

Step-by-step explanation:

Given : $a^2+\frac{1}{a^2}=18$

To find : The value of  $a-\frac{1}{a}$ ?

Solution :

Using identity,

$(x-y)^2=x^2+y^2-2xy$

Let $x=a$ and $y=\frac{1}{a}$

Substitute in the identity,

$(a-\frac{1}{a})^2=a^2+\frac{1}{a^2}-2\times a\times \frac{1}{a}$

$(a-\frac{1}{a})^2=18-2$

$(a-\frac{1}{a})^2=16$

Taking root both side,

$a-\frac{1}{a}=\pm 4$