Question

Root2+root3/3root2-2root3=2-b root6
Find the value of b (fast)

Answer 1

Answer:

Hi ,

It is given that ,

( √2 + √3 )/( 3√2 - 2√3 ) = a - b√6

LHS = ( √2+√3)/(3√2-2√3)

Rationalizing the denominator ,

= [(√2+√3)(3√2+2√3)]/[(3√2-2√3)(3√2+2√3)]

= [6+2√6 + 3√6 + 6 ]/[(3√2)²-(2√3)²]

= ( 12 + 5√6 )/( 18 - 12 )

= ( 12 + 5√6 )/6

= 12/6 + (5/6 ) √6

= 2 - ( - 5/6 ) √6 ----( 1 )

= a - b√6 ----( 2 )

Compare ( 1 ) and ( 2 ) , we get

a = 2 , b = - 5/6

I hope this helps you.

: )

Step-by-step explanation:

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