Find the value.

Algebra Level 2

IF x^{4} + 1/x^{4} = 119

then find the value of

x - 1/x = ?

3 2 4 5

View wiki
Vishwa Tej by Vishwa Tej , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

Ratnadip Kuri
Jan 16, 2015

x 4 + 1 x 4 = 119 x^4+\frac{1}{x^4}=119 => ( x 2 ) 2 + ( 1 x 2 ) 2 + 2 x 2 1 x 2 = 121 (x^2)^2+(\frac{1}{x^2})^2+2x^2\frac{1}{x^2}=121 => ( x 2 + 1 x 2 ) 2 = 1 1 2 (x^2+\frac{1}{x^2})^2=11^2 => x 2 + 1 x 2 = 11 x^2+\frac{1}{x^2}=11 => x 2 + 1 x 2 − 2 x 1 x = 9 x^2+\frac{1}{x^2}-2x\frac{1}{x}=9 => ( x − 1 x ) 2 = 3 2 (x-\frac{1}{x})^2=3^2 => x − 1 x = 3 x-\frac{1}{x}=3

3 Helpful 0 Interesting 0 Brilliant 0 Confused
Omkar Kulkarni
Jan 16, 2015

x 4 + 1 x 4 = 119 x^{4} + \frac {1}{x^{4}} = 119

x 4 + 2 + 1 x 4 = 121 x^{4} + 2 + \frac {1}{x^{4}} = 121

( x 2 + 1 x 2 ) 2 = 121 \left (x^{2} + \frac {1}{x^{2}} \right)^{2} = 121

x 2 + 1 x 2 = 11 x^{2} + \frac {1}{x^{2}} = 11

x 2 − 2 + 1 x 2 = 9 x^{2} -2 + \frac {1}{x^{2}} = 9

( x − 1 x ) 2 = 9 \left (x - \frac {1}{x} \right)^{2} = 9

x − 1 x = 3 x - \frac {1}{x} = \boxed {3}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...