Find the value of a and b if
7+√5/7-√5 - 7-√5+7+√5 = a+7/11 √5b
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Well, first you need to simplify your expression.
How ? Simple! By rationalising.
(7+√5)/(7-√5) - (7-√5)/7+√5)
Rationalise both the terms
(7+√5)² - (7-√5)²/ 49 - 5 = 49 + 14√5 + 5 - 49 + 14√5 - 5/ 44= 28√5/44= 7√5/11
Now, 7√5/11 = a + (7/11) √5b
On comparison, a = 0b = 1
How ? Simple! By rationalising.
(7+√5)/(7-√5) - (7-√5)/7+√5)
Rationalise both the terms
(7+√5)² - (7-√5)²/ 49 - 5 = 49 + 14√5 + 5 - 49 + 14√5 - 5/ 44= 28√5/44= 7√5/11
Now, 7√5/11 = a + (7/11) √5b
On comparison, a = 0b = 1
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