Question

if x= 2- under root 3 then find the value of
(i) x-1/x
(ii) x+1/x
(iii) x²+1/x²
(iv) x²-1/x²
(v) x³-1/x³

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Answer 1

Answer:

Step-by-step explanation:

x=2-√3

1/x=1/2-√3

=2+√3/(2-√3)(2+√3)

=2+√3/(4-3)

1/x=2+√3

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(i) x-1/x

=2-√3-(2+√3)

=2-√3-2-√3

=-2√3

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(ii) x+1/x

=2-√3+(2+√3)

=2-√3+2+√3

=4

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(iii) x²+1/x²

= x²+1/x²+2-2

=(x+1/x)²-2

=4²-2=16-2

=14

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(iv)

x²-1/x²=(x+1/x)(x-1/x)

=4*(-2√3)

=-8√3

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(v)

x³-1/x³=(x-1/x)(x²+1/x²+1)

=( -2√3)*(14+1) ( taking value from (iii) )

=-30√3

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