Find the value of a in the following :
5+2√3 / 7+4√3 = a - 6√3
Answers
Answer:
=a+b3
Since rationalization of c+da+b=c+da+b×c−dc−d
Taking L.H.S.
By rationalization,
7+435+23 = 7+435+23× 7−437−43
Since, {(a+b)(a−b)=a2−b2}
= [(7)2−(43)2](5+23
Step-by-step explanation:
Given :-
(5+2√3)/(7+4√3) = a-6√3
To find :-
Find the value of a ?
Solution:-
Given that :
(5+2√3)/(7+4√3) = a-6√3
On taking LHS :
(5+2√3)/(7+4√3)
The denominator = 7+4√3
The Rationalising factor of 7+4√3 = 7-4√3
On Rationalising the denominator then
=> [(5+2√3)/(7+4√3)]×[(7-4√3)/(7-4√3)]
=> [(5+2√3)(7-4√3)]/[(7+4√3)(7-4√3)]
=> [(5+2√3)(7-4√3)]/[7²-(4√3)²]
Since (a+b)(a-b) = a²-b²
=> [(5+2√3)(7-4√3)]/(49-48)
=> [(5+2√3)(7-4√3)]/(1)
=> [(5+2√3)(7-4√3)]
=> (5×7)+(5×-4√3)+(2√3×7)-(2√3×4√3)
=> 35-20√3+14√3-24
=> (35-24)+(14√3-20√3)
=> 11-6√3
Now given equation will be
=> 11-6√3 = a-6√3
On Comparing both sides then
=> a = 11
Answer:-
The value of a for the given problem is 11
Used formulae
- The Rationalising factor of a+√b is a-√b
- (a+b)(a-b) = a²-b²