Question

if x-1/x=7 find x^4+1/x^4

Answer 1

x-1/x=7
x-1=7x
6x=-1
x=-1/6
1/x=-6
x*x*x*x=1/1296
1/x to the power 4=1296
Now add 1/1296+1296 and you will get the answer

Answer 2

Ello!!

Here's your answer

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Given , x - 1 / x = 7

To find the value of x^4 + 1 / x^4

Now , x - 1 / x = 7

=> x - 1 = 7x

=> - 7x + x = 1

=> 6x = - 1

=> x = - 1 / 6

And , 1 / x = 1 / ( - 1 / 6 )

=> 1 / x = - 6

And , x + 1 / x = - 1 / 6 + ( - 6 )

=> - 1 / 6 - 6

= - ( 1 / 6 + 6 )

= - ( 1 + 36 / 6 )

= - 37 / 6

Now ,

x^4 + 1 / x^4

= ( x^2 )^2 + ( 1 / x^2 )^2

[ • ( a )^2 + ( b )^2 = ( a + b )^2 - 2ab → Using this identity ]

= ( x^2 + 1 / x^2 ) - 2 × x^2 × 1 / x^2

= { ( x )^2 + ( 1 / x )^2 } - 2

= { ( x + 1 / x )^2 - 2 × x × 1 / x } - 2

= { ( 37 / 6 )^2 - 2 } - 2

= { 1369 / 36 - 2 } - 2

= { 1369 - 72 / 36 } - 2

= ( 1297 / 36 ) - 2

= 1297 - 36 / 36

= 1261 / 36

= 35.02

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Hope it helps you dear!

★ Devil king