Question

if a and b are rational numbers and 3+4√8/3+5√8=a+b√8 then find the values of a and b

Answer 1

3 + 4√8/3 + 5√8 = a + b√8

3 + 4√8 * ( 3 - 5√8)/3+5√8 * (3 - 5√8)

= 9 - 15√8 + 12√8 - 20√8/3^2 - 5√8

= 9 - 3√8 - 20√8/9 - 200

= 9 - 23√8/-191

Therefore, a = 9/191 and b = -23/191 and then √8.

Hope it helps :)

Answer 2

 3 + 4√8    =    (3 + 4√8) (3 - 5√8)    =    9 - 15√8 + 12√8 - 160  

 3 + 5√8           (3 + 5√8) (3 - 5√8)             3² - (5√8)²

 9 - 15√8 + 12√8 - 160     = -151 - 3√8   =    151 + 3√8  

      9 - 200                              - 192                   192

a = 151/192

b = 3/192  = 1/64