Question
If {x + (1/x)} = 8, then find the value of {x 4
+ (1/x 4 )}.Solution
{x + (1/x)} = 8
Squaring both sides,
Using (a + b) 2 = a 2 + 2ab + b 2
{x + (1/x)} 2 = 8 2
So, x 2 + (1/x 2 ) + 2 × (x) × (1/x) = 64
Or, x 2 + (1/x 2 ) + 2 = 64
Or, x 2 + (1/x 2 ) = 64 – 2 = 62
Again squaring both sides,
{x 2 + (1/x 2 )} 2 = 62 2
So, x 4 + (1/x 4 ) + 2 × (x 2 ) × (1/x 2 ) = 3844
Or, x 4 + (1/x 4 ) + 2 = 3844
Or, x 4 + (1/x 4 ) = 3844 – 2 = 3842
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