find the values of A and B such that 5 + 2 root 6 by 5 minus 2 root 6 is equal to a + b root 6 where A and B are rational numbers
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Answer:
a = 49, b = 10.
Step-by-step explanation:
5 + 2√6/5-2√6
Multiply numerator and denominator by 5 + 2√6
= (5 + 2√6)(5 + 2√6) / (5 + 2√6)(5 - 2√6)
= (5 + 2√6)²/ 25 - 24
= (5 + 2√6)²
= 25 + 24 + 10√6
= 49 + 10√6
Given, this is equal to a + b√6
=> 49 + 10√6 = a + b√6
=> a = 49, b = 10.
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