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If a and b are rational numbers and 5 + 2 root 6 by 5 - 2√6 equals to a + b√6 then find the values of a and b?
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If a and b are rational numbers and 5 + 2 root 6 by 5 - 2√6 equals to ...
Given Expression:
5 + 2√6 / 5 - 2√6

Let's rationalize the denominator:
Multiplying the numerator and denominator by the conjugate of the denominator:
= (5 + 2√6)(5 + 2√6) / (5 - 2√6)(5 + 2√6)
= (25 + 20√6 + 24) / (25 - 24)

Simplify the expression:
= (49 + 20√6) / 1
= 49 + 20√6

Therefore, a = 49 and b = 20.

Explanation:
The given expression can be simplified to 49 + 20√6 after rationalizing the denominator. This form matches the expression a + b√6 with a = 49 and b = 20. Therefore, the values of a and b are 49 and 20, respectively.
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