Question

3
Find the value of a
in the equation,(3+4√3)(2-a√3)=-18+2√3​

Answer 1

Given:

The equation is:

`\left(3+4√(3)\right)\left(2-a√(3)\right)=-18+2√(3)`

To find:

The value of a.

Solution:

We have,

`\left(3+4√(3)\right)\left(2-a√(3)\right)=-18+2√(3)`

On simplification, we get

`(3)(2)+(4√(3))(2)+(3)(-a√(3))+(4√(3))(-a√(3))=-18+2√(3)`

`6+8√(3)-3a√(3)-4a(3)=-18+2√(3)`

`6+8√(3)-3a√(3)-12a=-18+2√(3)`

`(6-12a)+(8-3a)√(3)=-18+2√(3)`

On comparing both sides, we get

`6-12a=-18`

`-12a=-18-6`

`a=(-24)/(-12)`

`a=2`

And,

`8-3a=2`

`-3a=2-8`

`a=(-6)/(-3)`

`a=2`

Therefore, the value of a is 2.