find the value of a and b if 5+2√3/7+4√3=a+b√3
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Solution
Given :-
- a + b√3 = (5+2√3)/(7+4√3)
Find :-
- Value of a & b
Explanation
First rationalize denominator of (5+2√3)/(7+4√3)
==> (5+2√3)(7-4√3)/(7+4√3)(7-4√3)
==> (35-20√3+14√3-24)/(7²-16*√3²)
==> (11-6√3)/(49-48)
==> (11-6√3)
So, Now
==> a + b√3 = (11-6√3).
Now Compare both sides
We find , here
- a = 11
- b = -6
Hence
- Value of a = 11
- Value of b = -6
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