Question

If x+1/x=9 and x-1/x=6, then find the value of x´-1/x´.​

Answer 1

Step-by-step explanation:

Answer

Consider x+

x

1

=9, squaring both sides we get,

(x+

x

1

)

2

=9

2

⇒x

2

+(

x

1

)

2

+(2×x×

x

1

)=81(∵(a+b)

2

=a

2

+b

2

+2ab)

⇒x

2

+

x

2

1

+2=81

⇒x

2

+

x

2

1

=81−2

⇒x

2

+

x

2

1

=79

We know that (a−b)

2

=a

2

+b

2

−2ab, substitute a=x and b=

x

1

as shown below:

(x−

x

1

)

2

=x

2

+(

x

1

)

2

−(2×x×

x

1

)

=79−2(∵x

2

+

x

2

1

=79)

=77

Therefore,

(x−

x

1

)

2

=77

⇒x−

x

1

=±

77

Hence, x−

x

1

=±

77

.

Answer 2

$\color{red}\huge{\underline{\underline{\bf GIVEN\dag}}}$

• $\sf{x + \frac{1}{x} = 9....(1) }$
• $\sf{x - \frac{1}{x} = 6....(2)}$

$\color{red}\huge{\underline{\underline{\bf SOLUTION\dag}}}$

$\sf{ \purple{adding \: (1) \: and \: (2) : }}$

$\implies \sf{2x} = 15$

$\therefore \sf{x = \frac{15}{2} }$

$\sf{ \purple{now \: substitue \: x \: in : }}$

$\sf{ {x}^{2} - \frac{1}{ {x}^{2} } }$

$\implies \sf {( \frac{15}{2} )}^{2} - \frac{1}{ ({ \frac{15}{2} )}^{2} }$

$\implies \sf {\frac{225}{4} } - \frac{4}{ 225 }$

$\implies \sf{56.25 - 0.017}$

$\orange{ \boxed{ \therefore{\sf{ {x}^{2} - \frac{1}{ {x}^{2} } } = 56.2 \: \: (or) \: \: \frac{281}{5} }}}$