Let `alphaa n dbeta` be the solutions of the quadratic equation `x 62-1154 x+1=0` , then the value of `alpha4+beta4` is equal to ______.

Answer

6

Explanation

`alpha+beta=1154andalphabeta=1`
`(sqrtalpha+sqrtbeta)^(2)=alpha+beta+2sqrt(alphabeta)=1154+2=1156=(34)^(2)`
`impliessqrtalpha+sqrtbeta=34`
Again `(alpha^(1//4)+beta^(1//4))^(2)=sqrtalpha+sqrtbeta+2(alphabeta)^(1//4)=34+2=36`
`alpha^(1//4)+beta^(1//4)=6`