Question

(3+√7)/(3-√7)=2a+3b√7
Find the value of a and b

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Answer 1

Step-by-step explanation:

= (3+√7)/(3-√7)

= (3+√7)²/(3²-√7²)

= (9 + 6√7 + 7)/(9-7)

= (16 + 6√7)/2

= 8 + 3√7

= 2*4 + 3√7

= 2a + 3b√7

=> a = 4, b = 1

Answer 2

Answer:

3+√7 / 3-√7

multiply 3+√7 on both numerator and denomerator

 (3+√7)² /  (3-√7)(3+√7) = a+b√7

⇒9 + 7 + 6√7 / 3² -√7²   = a+b√7

⇒16+ 6√7 / 9-7              =a+b√7

⇒16+ 6√7 / 2                  =a+b√7

⇒2(8+3√7)/2                  =a+b√7

⇒8 +3√7                          =a+b√7

on compairing both sides

a=8

b=3