Question

find the rationale no. a and b such that 1/2+√3=a+b√3​

Answer 1

(a−1)

2

​

+3=b

2

​

+a

Since a,b are rational and

2

​

is irrational, we can compare rational and irrational terms both sides.

Comparing terms attached to

2

​

both sides we get,

⇒ a−1=b ---- ( 1 )

Comparing rational terms both sides gives

⇒ 3=a ---- ( 2 )

Substituting ( 2 ) in ( 1 ),

⇒ 3−1=b

∴ b=2

⇒ a+b=3+2=5

Answer 2

Answer:

a−1)

2

+3=b

2

+a

Since a,b are rational and

2

is irrational, we can compare rational and irrational terms both sides.

Comparing terms attached to

2

both sides we get,

⇒ a−1=b ---- ( 1 )

Comparing rational terms both sides gives

⇒ 3=a ---- ( 2 )

Substituting ( 2 ) in ( 1 ),

⇒ 3−1=b

∴ b=2

⇒ a+b=3+2=5