Question

If x=√3-1/√3+1 and y=2+√3/2-√3, find the value of x+y.

Answer 1

Heya ✋

x = √3 - 1 / √3 + 1

= (√3 - 1) × (√3 - 1) / (√3 + 1) × (√3 - 1)

= (√3 - 1)^2 / (√3)^2 - (1)^2

= (√3)^2 + (1)^2 - 2 × √3 × 1 / 3 - 1

= 3 + 1 - 2√3 / 2

= 4 - 2√3 / 2

= 2 - √3

y = 2 + √3 / 2 - √3

= (2 + √3) × (2 + √3) / (2 - √3) × (2 + √3)

= (2 + √3)^2 / (2)^2 - (√3)^2

= (2)^2 + (√3)^2 + 2 × 2 × √3 / 4 - 3

= 4 + 3 + 4√3

= 7 + 4√3

Therefore ,

x + y

= (2 - √3) + (7 + 4√3)

= 2 - √3 + 7 + 4√3

= 2 + 7 - √3 + 4√3

= 9 + 3√3

= 3(3 + √3)


Thanks :)))))