find b if √2+√3/3√2+3√3=2-b√6
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There are two ways to approach this question.
First is to rationalize both a and b, and then find out the answer by squaring and adding them.
We get a = 5 + 2.sqrt(6), b = 5 - 2.sqrt(6).
So a^2 + b^2 = 25 + 24 + 25 + 24 = 98.
The second approach, is to observe that a = 1/b.
So a^2 + b^2 = a^2 + (1/a)^2 = (a + 1/a)^2 - 2.a.(1/a) = (10)^2 - 2 = 98.
First is to rationalize both a and b, and then find out the answer by squaring and adding them.
We get a = 5 + 2.sqrt(6), b = 5 - 2.sqrt(6).
So a^2 + b^2 = 25 + 24 + 25 + 24 = 98.
The second approach, is to observe that a = 1/b.
So a^2 + b^2 = a^2 + (1/a)^2 = (a + 1/a)^2 - 2.a.(1/a) = (10)^2 - 2 = 98.
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