If (√2 + √3)/(3√2 - 2√3) = a - b√6, then find the value of a and b.
Answers
Answered by
2
Step-by-step explanation:
Given:-
To Find:-
- Find the value of a and b
Solution:-
By rationalizing the denominator:-
Answered by
3
Data :
(√2 + √3)/(3√2 - 2√3) = a - b√6
Solving :
= ( √2 + √3 / 3 √2 - 2 √3 ) × ( 3 √2 + 2 √3 / 3 √2 + z √3 ) = a - b √6
= [ √2 ( 3 √2 ) + √2 ( 2 √3 ) + √3 ( 3 √2 ) + √3 ( 2 √3 ) ] / [ ( 3 √2 )^2 - ( 2 √3 )^2 ] = a - b √6
= ( 6 + 2 √6 + 3 √6 + 6 ) / ( 18 - 12 ) = a - b √6
= ( 6 + 6 + 2 √6 + 3 √6 ) / 6 = a - b √6
= ( 12 + 5 √6 ) / 6 = a - b √6
= 2 + 5 √6 / 6 = a - b √6
= Form = a - b √6
So, a = 2
a = 2 b = -5 / 6
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