What is the correct answer ?

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3 Answers
Mar 3, 2018

#(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)"#

Mar 3, 2018

See below.

Explanation:

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

Mar 3, 2018

#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#