Question

if x^2+1/x^2=66 then x-1/x=​

Answer 1

Answer: 8

Step-by-step explanation:

x²+(1/x²)=66 (Given)

Now we know that

[x-(1/x)]² = x²+(1/x²) -2 ( By using (a+b)²= a²+b²+2ab)

So [x-(1/x)]² = 66-2

[x-(1/x)]² = 64

[x-(1/x)] = sq.rt 64

[x-(1/x)] = 8.

Thanks.

Hope it helps.

Answer 2

Step-by-step explanation:

$\bf \underline{Solution-}$

$\sf{ {x}^{2} + \frac{1}{ {x}^{2} } = 66}$

$\bf \underline{To find-}$

$\sf{the \: value \: of :\: x - \frac{1}{x} = \: ?}$

$\bf \underline{Solution-}$

$\sf {\bigg(x - \frac{1}{x} \bigg) ^{2} = {x}^{2} + \frac{1}{ {x}^{2} } - 2 \: \: \: \: \: \: [ \because \: (a - b {)}^{2} = {a}^{2} + {b}^{2} - 2ab ]} \\ \\ = 66 - 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\rm{ [ \because {x}^{2} + \frac{1}{ {x}^{2}} = 66 \:(Given) ] }$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:= 64$

$\sf{ \therefore \: \: \: \: \: \: x - \frac{1}{x} = \sqrt{64} } \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = ± \: 8$

$\bf\underline{Hence,the \: value \: of : \: x - \frac{1}{x} \: is \: ± \: 8.}$