Question

Can any one plz tell 21 sum

Answer 1

Given 1/2 + root 3 + 2/root 5 - root 3 + 1/2 - root 5.

LCM = (2 + root 3)(root 5 - root 3)(2 - root 5)

=  1 * (2 - root 5)(root 5 - root 3)/(2 + root 3)(2 - root 5)(root 5 - root 3) + 2 * (2 + root 3)(2 - root 5)/(2 + root 3)(2 - root 5)(root 5 - root 3) + 1 * (2 + root 3)(root 5 - root 3)/(2 + root 3)(2 - root 5)(root 5 - root 3)


= 1 * (2 - root 5)(root 5 - root 3) + 2(2 + root 3)(2 - root 5) + 1 * (2 + root 3)(root 5 - root 3)/(2 + root 3)(2 - root 5)(root 5 - root 3)


On solving the numerator we get

= (2 - root 5)(root 5 - root 3) + 2(2 + root 3)(2 - root 5) + (2 + root 3)(root 5 - root 3)


= (2 root 5 - 2 root 3 - root 5 root 5 + root 5 root 3) + 2(4 - 2 root 5 + 2 root 3 - root 15) + (2 root 5 - 2 root 3+ root 15 - 3)


= (2 root 5 - 2 root 3 - 5 + root 15) + (8 - 4 root 5 + 4 root 3 - 2 root 15) + (2 root 5 - 2 root 3 + root 15 - 3)


= 2 root 5 - 2 root 3 - 5 + root 15 + 8 - 4 root 5 + 4 root 3 - 2 root 15 + 2 root 5 - 2 root 3 + root 15 - 3


= 2 root 5 - 2 root 3 + 2 root 5 - 2 root 3 - 3 - 4 root 5 + 4 root 3 - 5 + 8


= 2 root 5 + 2 root 5 - 3 - 4 root 5 - 5 + 8


= - 3 - 5 + 8


= 0


If the Numerator is 0. Then the total answer will be 0. No need to calculate the denominator.


Hope this helps!