Question

pls answer this question

Answer 1

x = √2 + 1/√2 - 1

Rationalise

√2 + 1/√2 - 1 × √2 + 1/ √2 + 1

= (√2 + 1)^2/ (√2)^2 - (1)^2

= 2 + 2√2 + 1/ 2 - 1

= 3 + 2√2

Similary,

y = √2 - 1/√2 + 1

Rationalise

y = √2 - 1/√2 + 1 × √2 - 1/√2 - 1

= (√2 - 1)^2/(√2)^2 - (1)^2

= 2 - 2√2 + 1/ 2 - 1

= 3 - 2√2

Now,

(x - y)^2 - 2xy

= (3 + 2√2 - 3 + 2√2)^2 - 2(3 + 2√2)(3 - 2√2)

= (4√2)^2 - 2[ (3)^2 - (2√2)^2]

= 16*2 - 2[9-8]

= 32 - 2

= 30.