Given info:- Rationalise the denominator and find out the value of "a" and "b"
Given expression: {(5-2√6)/(5+2√6)} = a+b√3
Explanation:-
{(5-2√6)/(5+2√6)} = a+b√3
We know that Rationalising factor of a+b√c is a-b√c.
Therefore, the rationalising factor of 5+2√6 is 5-2√6.
⇛{(5-2√6)/(5+2√6)} × {(5-2√6)/(5-2√6)} = a+b√3
⇛{(5-2√6)(5-2√6)}/{(5+2√6)/(5-2√6)} = a+b√3
⇛{(5-2√6)²}/{5+2√6)(5-2√6)} = a+b√3 [∵(a-b)(a-b)=(a-b)²]
⇛{(5-2√6)²}/{(5)²-(2√6)²} = a+b√3 [∵(a+b)(a-b)=a²-b²]
⇛{(5-2√6)²}/({5*5)-(2*2√6*6)} = a+b√3
⇛{(5-2√6)²}/(25 - 4√6) = a+b√3
⇛{(5-2√6)²}/(25-24) = a+b√3
⇛{(5-2√6)²}/1 = a+b√3
⇛(5-2√6)² = a+b√3
⇛(5)²-(2√6)²+2(5)(2√6) = a+b√3
⇛(5*5) - (2*2√6*6) - 10 - 2√6 = a+b√3
⇛25 - 10 - 4√6 - 2√6 = a+b√3
⇛15 - 4√6 - 2√6 = a+b√3
⇛15 + 6√6 = a+b√3
∴ 15 + 6√6 = a+b√3
On, comparing with both RHS we notice that:
The value of a = 15 and b = 6.
Hope this helps!!
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