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