Question

please can you let me it's answer.
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Answer 1

Solution:

It is given that,

x = √3 + √2 ----(1)

1/x = 1/(√3+√2)

= (√3-√2)/[(√3+√2)(√3-√2)]

= (√3-√2)/[(√3)²-(√2)²]

= (√3-√2)/(3-2)

= √3-√2 -----(2)

Now ,

i) x + 1/x

= √3+√2+√3-√2

= 2√3 ----(3)

ii ) x - 1/x

= √3+√2-(√3-√2)

= √3+√2-√3+√2

= 2√2 -----(4)

iii) x² - x^-2

=x² - (1/x)²

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

= 2√3 × 2√2

= 4√6

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