Question

If 2+√3/3√2-2√3=a+b√6 find the value of a&b

Answer 1

Heya !!!


✓2 + ✓3 / 3✓2 - 2✓3 = A + B✓6




LHS = ( ✓2 + ✓3 ) / ( 3✓2 - 2✓3 )




Rationalizing the denominator ( 3✓2 - 2✓3 )


=> ( ✓2 + ✓3 ) / ( 3✓2 - 2✓3) × ( 3✓2 + 2✓3 ) / ( 3✓2 + 2✓3 )




=> ( ✓2 + ✓3 ) ( 3✓2 - 2✓3 ) / ( 3✓2 + 2✓3 ) ( 3✓2 - 2✓3 )


we know that,

( A+ B) ( A - B ) = A² - B²

=> ✓2 ( 3✓2 + 2✓3 ) + ✓3 ( 3✓2 + 2✓3 ) / (3✓2)² - (2✓3)²



=> 6 + 2✓6 + 3✓2 + 6 / 18 - 12


=> 12 + 5✓6/6


Now,

LHS = RHS


12 + 5✓6/6 = A - B✓6



Clearly,



A = 12/6 = 2 and B = -5/6.



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