if x+1/x=4, find the value of x^4+ 1/x^4
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Hey !!
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x + 1/x = 4
On squaring both sides
[x + 1/x]2 = 16
Using the identity
[ x + 1/x ]2 = x2 + 1/x2 + 2
16 - 2 = x2 + 1/x2
Hence x2 + 1/x2 = 14 [ 1 ]
Now !
x
Squaring both sides of [1 ]
[ x2 + 1/x2 ]2 = 196
196 = x4 + 1/x4 + 2
Hence the value of x4 +1/x4 = 196 - 2 = 194✔
Hope it helps you☺
_______________________
x + 1/x = 4
On squaring both sides
[x + 1/x]2 = 16
Using the identity
[ x + 1/x ]2 = x2 + 1/x2 + 2
16 - 2 = x2 + 1/x2
Hence x2 + 1/x2 = 14 [ 1 ]
Now !
x
Squaring both sides of [1 ]
[ x2 + 1/x2 ]2 = 196
196 = x4 + 1/x4 + 2
Hence the value of x4 +1/x4 = 196 - 2 = 194✔
Hope it helps you☺
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