Question

root3+4root2 divide by 3 root2+5 root 3=a-b
root3

Answer 1

Step-by-step explanation:

(√3 + 4√2 ) / ( 3√2 + 5√3 ) = a - b√3

First of all ,

( √3 + 4√2 )( 3√2 - 5√3 ) [ Rationalising Numerator ]

» 3√6 + 4 × 2 - 5 × 3 - 20√6

» - 17√6 - 7

( 3√2 + 5√3 )( 3√2 - 5√3 ) [ Rationalising Denominator ]

» ( 3√2 )² - ( 5√3 )²

» 18 - 75

» - 57

Now combinig Rationalised numerator and Denominator ( I did this because it could look creepy if I was doing it as a fraction )

»» (17√6 + 7 ) / 57 = a - b√3

Therefore, a = 7 / 57

b = 17√2 / 57