Question

If x = (√3-7)/(√3+7) and y = (3+2√2)/(3-2√2) then find the value of x+y

Answer 1

x = (√3-7)/(√3+7)

→ (√3-7)/(√3+7)×(√3-7)/(√3-7)

→ (√3-7)²/(√3+7)(√3-7)

→ [√3²+7²-2(√3)(7)]/(√3²-7²)

→ (3+49-14√3)/(3-49)

→ (52-14√3)/(-46)

→ -(52-14√3)/46

→ -52/46 + 14√3/46

→ -26/23 + 7√3/23

→ (-26+7√3)/23

y = (3+2√2)/(3-2√2)

→ (3+2√2)/(3-2√2)×(3+2√2)/(3+2√2)

→ (3+2√2)(3+2√2)/(3-2√2)(3+2√2)

→ (3+2√2)²/(3²-(2√2)²)

→ [3²+(2√2)²+2(3)(2√2)]/(9-4(2))

→ (9+8+12√2)/(9-8)

→ 17+12√2

x+y = (-26+7√3)/23 + 17+12√2

= (-26+7√3)/23 + (17+12√2)×23/23

= [-26+7√3+161+276√2]/23

= [135 + 7√3 + 276√2]/23

Hope it helps