Question

What is the correct answer ?

Answer 1

`(A) -(sqrt(7)+7)/3`

Explanation:

`"Multiply numerator and denominator by "1+sqrt(7)" : "`

`= (2 sqrt(7) (1+sqrt(7)))/((1-sqrt(7))(1+sqrt(7)))`

`"Now apply "(a-b)(a+b) = a^2-b^2" : "`

`= (2 sqrt(7) (1+sqrt(7)))/(1-7)`
`= (2 sqrt(7) (1+sqrt(7)))/-6`
`= - (sqrt(7) (1+sqrt(7)))/3`
`= -(sqrt(7)+7)/3`

`=> " Answer (A)"`

Answer 2

See below.

Explanation:

`(2 sqrt7)/(1-sqrt7) = (2 sqrt7)/(1-sqrt7) ((1+sqrt7)/(1+sqrt7)) = (2sqrt7+14)/(1-7) =- (sqrt7-7)/3`

Answer 3

`A`

Explanation:

To find the answer we must rationalise the denominator.

We are given:
`(2sqrt(7))/(1-sqrt(7))`

We must multiply the top and bottom by `1+sqrt(7)` since it will cancel out the square root on the bottom.

`(2sqrt(7))/(1-sqrt(7))*(1+sqrt(7))/(1+sqrt(7))=(2sqrt(7)(1+sqrt(7)))/((1-sqrt(7))(1+sqrt(7)))=(2sqrt(7)+14)/(1+sqrt(7)-sqrt(7)-7)=(2sqrt(7)+14)/(-6)=-(2sqrt(7)+14)/6=-(sqrt(7)+7)/3-=A`