Question

find the value of a and b if
$\frac{1}{4 + \sqrt{15} } = a \: + \: b \: = \: 15$
​

Answer 1

7+4

3

5+2

3

=a+b

3

Since rationalization of

c+

d

a+

b

=

c+

d

a+

b

×

c−

d

c−

d

Taking L.H.S.

By rationalization,

7+4

3

5+2

3

=

7+4

3

5+2

3

×

7−4

3

7−4

3

Since, {(a+b)(a−b)=a

2

−b

2

}

=

[(7)

2

−(4

3

)

2

]

(5+2

3

)×(7−4

3

)

=

49−16

3

3

35+14

3

−20

3

−8

3

3

=

49−48

35−

3

(14−8)−24

=

1

35−

3

(6)−24

=11−6

3

Hence, by comparing a = 11 & b = -6.