Question

log question class 11​

Answer 1

Answer:

0

Step-by-step explanation:

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

Then Log(1) = 0

Answer 2

please see the attachment