If (x + 1/x) = 3, then find the value of: a) (x² + 1/x²) and b) (x⁴ + 1/x⁴). (4 marks)
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Answer:
x²+1/x²= 7
x⁴+1/x⁴ = 47
Step-by-step explanation:
x+1/x = 3
=> (x+1/x)² = 9
=> x²+1/x²+2*x*1/x = 9
=> x²+1/x²+2 = 9
=> x²+1/x² = 9-2
=> x²+1/x²= 7
(x²+1/x²)²= 7²
=> x⁴+1/x⁴+2*1/x²*x² = 49
=> x⁴+1/x⁴+2 =49
=> x⁴+1/x⁴ = 49-2
=> x⁴+1/x⁴ = 47
using formula (x+y)² = x²+y²+2*x*y
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