Question

If x = 9 - 4 root 5 , find x^2 - 1/ x^2 and x^3 + 1/x^3 .

Answer 1

x=9-4√5
∴, 1/x=1/(9-4√5)
=(9+4√5)/(9-4√5)(9+4√5)
=(9+4√5)/{(9)²-(4√5)²}
=(9+4√5)/(81-80)
=9+4√5
∴, x²-1/x²
=(x+1/x)(x-1/x)
=(9-4√5+9+4√5)(9-4√5-9-4√5)
=(18)(-8√5)
=-144√5
x³+1/x³
=(x+1/x)³-3·x·1/x(x+1/x)
=(9-4√5+9+4√5)³-3(9-4√5+9+4√5)
=(9)³-3(9)
=729-27
=702

Answer 2

Answer:

Step-by-step explanation:

X=9-4√5

∴, 1/x=1/(9-4√5)

=(9+4√5)/(9-4√5)(9+4√5)

=(9+4√5)/{(9)²-(4√5)²}

=(9+4√5)/(81-80)

=9+4√5

∴, x²-1/x²

=(x+1/x)(x-1/x)

=(9-4√5+9+4√5)(9-4√5-9-4√5)

=(18)(-8√5)

=-144√5

x³+1/x³

=(x+1/x)³-3·x·1/x(x+1/x)

=(9-4√5+9+4√5)³-3(9-4√5+9+4√5)

=(9)³-3(9)

=729-27

=702

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