Question

If both a and b are rational numbers, then find the
values of a and b in each case.
(0)
√3-1
13+1
= a +b root3​

Answer 1

Answer:

(a)

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

(b)

Rationalizing the LHS of

7−4

3

5+

3

=47a+b

3

.

7−4

3

5+

3

=47a+b

3

7−4

3

5+

3

×

7+4

3

7+4

3

=47a+b

3

(7)

2

−(4

3

)

2

(5+

3

)(7+4

3

)

=47a+b

3

49−48

35+20

3

+7

3

+12

=47a+b

3

47+27

3

=47a+b

3

By comparing both sides,

a=1,b=27