Question

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

Answer 1

Answer:

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Step-by-step explanation:

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.