Question

if x=sqrt(-3)/2 , find the value of sqrt(1+x)+sqrt(1-x)/sqrt(1+x)-sqrt(1-x)

Answer 1

cant take the sqrt of neg num
is it supposed to deal with complex num

Answer 2

oh sorry, its written as x=sqrt(3)/2

Answer 3

i made a mistake
it simplifies to
\[\frac{1+\sqrt{1-x^{2}}}{x}\]
\[x=\frac{\sqrt{3}}{2}\]
\[=\sqrt{3}\]

Answer 4

could you please provide some info on how we get 1+sqrt(1-x^2)/x ?

Answer 5

multiply by conjugate on top and bottom
then combine like terms

Answer 6

conjugate is sqrt(1+x) + sqrt(1-x)

Answer 7

got till 1+x+1-x+2sqrt(1-x^2)/(1-x)+(1-x)