Question

find the value of a and b if 3+✓7 /3-✓7 = a+b ✓7​

Answer 1

Answer:

Step-by-step explanation:

3+√7 / 3-√7

multiply 3+√7 on both numerator and denonemeter

(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

Answer 2

Answer:

a=8 and b=3...

Step-by-step explanation:

Rationalizing the LHS of

3−

7

3+

7

=a+b

7

.

3−

7

3+

7

×

3+

7

3+

7

=a+b

7

(3)

2

−(

7

)

2

(3+

7

)

2

=a+b

7

9−7

9+7+6

7

=a+b

7

2

16+6

7

=a+b

7

8+3

7

=a+b

7

By comparing both sides,

a=8,b=3