if 5+2√3 / 7+4√3 = a+b√3 then find a and b
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Step-by-step explanation:
Given expression
The denominator is 7 + 4√3.
We know that
Rationalising factor of a + b√c = a - b√c.
So, the rationalising factor of 7 +4√3 = 7-4√3.
On rationalising the denominator them
Now, applying algebraic identity in denominator because it is in the form of;
(a+b)(a-b) = a² - b²
Where, we have to put in our expression: a = 7 and b = 4√3 , we get
Subtract 49 from 48 in denominator to get 1.
Now, multiply both term left side to right side.
On, comparing with R.H.S , we have
a = 11 and b = -6
Used Formulae:
(a+b)(a-b) = a² - b
Rationalising factor of a + b√c = a - b√c.
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