Find the value of a and b
1)√2+√3
_____ = 2-b√6
3√2-2√3
please it's urgent!!!
Answers
Step-by-step explanation:
Given:-
(√2+√3)/(3√2-2√3) = a-b√6
To find:-
Rationalised the denominator and find out the value of a and b.
Solution:-
Given that
(√2+√3)/(3√2-2√3) = a-b√6
Denominator = 3√2-2√3
We know that
Rationalising factor of a√b-a√b = a√b+a√b
Rationalising factor of 3√2-2√3 = 3√2+2√3
On Rationalising the denominator then
=> [(√2+√3)/(3√2-2√3)]×[(3√+2√3)/(3√2+2√3)]
=> [(√2+√3)(3√2+2√3)]/[(3√2-2√3)(3√2+2√3)]
Now, multiplying numerator left side to right side we get,
=> [3(√2×2)+2(√3×2)+3(√2×3)+2(√3×3)]/[(3√2-2√3)(3√2+2√3)]
Now, applying algebraic identity in denominator
We know that
(a-b)(a+b)=a^2-b^2
Where a = 3√2 and b=2√3
=> (3×2+2√6+3√6+2×3)/[(3√2)^2-(2√3)^2]
=> (12+5√6)/(18-12)
=> 12+5√6/6
=> 2+⅚√6
∴ a-b√6 = 2+⅚√6
On, comparing with R.H.S
- a = 2,
- b = -⅚√6 = -⅚
Answer:-
Hence, the value of a = 2 and b = -5/6.
Used formulae:-
- Rationalising factor of a√b-a√b = a√b+a√b
- (a-b)(a+b)=a^2-b^2
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