If x = √3-√2/√3+√2 and y = √3+√2/√3-√2 find the value of x3+y3 :

(1) 807 (2) 907 (3) 970 (4)870

Solution:

Rationallsing the denominators. we have

x=√3-√2/√3+√2*√3-√2/√3-√2

=(√3-√2)²/(√3)²-(√2)²

= 3+2-2√3*√2/3-2 = 5-2√6

and,  y=√3+√2/√3-√2*√3+√2/√3+√2

= (√3+√2)²/(√3)²-(√2)²

= 3+2+2√3*√2/3-2 = 5+2√6

:.  x+ y

= 5-2√6+5+2√6 = 10

and,  xy= (5-2√6) (5+2√6)

= 5²-(2√6)² =25-24=1

x³+y³ =(x+y)³-3xy (x+ y)

= 10³– 3 *10

= 1000 – 30 =970

Then the option is (3)