Question
If [x + (1/x)] = 7, find the value of [x⁴ +
(1/x⁴)].Solution
ATQ,
x + (1/x) = 7
Squaring both sides:
[x + (1/x)]² = 7²
Using identity: (a + b)² = a² + 2ab + b²
x² + (1/x²) + 2 = 49
So, x² + (1/x²) = 49 - 2 = 47
Squaring again:
[x² + (1/x²)]² = 47² = 2,209
So, x⁴ + (1/x⁴) + 2 = 2,209
Therefore, x⁴ + (1/x⁴) = 2,209 - 2 = 2,207
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