Find the values of a and b if 7+3√5/3+√5 - 7-3√5/3-√5 = a+b√5

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Solution

7+3√5/(3+√5) - 7-3√5/(3-√5) a + √5b
= (7+3√5)(3-√5) - (7-3√5)(3+√5)/(3+√5)(3-√5) = a + √5b
21-7√5+9√5-15-21-7√5+9√5+15/9-5 = a + √5b
4√5/4 = a + √5b
√5 = a + √5b
Comparing both left and right hand side a = 0 and b = 1
Thus a = 0 and b= 1 answer.

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