if x^4+1/x^3=47 find x^3+/1x^3
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x⁴+1/x⁴ = 47
=> (x²)²+(1/x²)²+2(x²)(1/x²) = 49
=> using formula => (a²+b²+2ab) = (a+b)²
=> (x²+1/x²)² = 7²
=> cancellation of square on both sides
=> x²+1/x² = 7
(x²+1/x²)+2(x)(1/x) = 9
=> (x+1/x)² = 3²
cancellation if square on both sides
=> x+1/x = 3
x³+1/x³ = (x+1/x)(x²+1/x²-(x)(1/x))
=> x³+1/x³ = 3(7-1) => 3(6) => 18
hope this helps
=> (x²)²+(1/x²)²+2(x²)(1/x²) = 49
=> using formula => (a²+b²+2ab) = (a+b)²
=> (x²+1/x²)² = 7²
=> cancellation of square on both sides
=> x²+1/x² = 7
(x²+1/x²)+2(x)(1/x) = 9
=> (x+1/x)² = 3²
cancellation if square on both sides
=> x+1/x = 3
x³+1/x³ = (x+1/x)(x²+1/x²-(x)(1/x))
=> x³+1/x³ = 3(7-1) => 3(6) => 18
hope this helps
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