Question

the value of 2/√5-√3 is​

Answer 1

Answer:

We know (A+B)^3 = A^3 + B^3 + 3AB(A+B)

Now put A=( 2+5 )^1/3 and B=( 2-5 )^1/3

So now after substituting we have

{ (2+5 )^1/3 + (2-5)^1/3 }^3

= 2+5 +2 -5 + 3(2+5)(2-5)[ (2+5 )^1/3 + (2-5)^1/3) ]

You want to find ( 2+5 )^1/3 + ( 2-5 )^1/3

let’s take it as X

Now it is X^3 = 4 + 3*(2+5)(2-5)*X

i.e. X^3 = 4 + 3*(4-5)*X

i.e. X^3 = 4 - 3*X

This cubic equation has only one real solution which is “1”.

So, [ ( 2+5 )^1/3 + ( 2-5 )^1/3 ] = 1

Answer 2

$\huge\implies\frac{2}{\sqrt{5}} - \sqrt{3}$

$\huge\implies{2 × \sqrt{5}} - \frac{\sqrt{3}}{2}$