IIT JEE , AIEEE Forum - Mathematics , Algebra - solve this one if you are good in quadratics by shortest methood

ziauddin75

16x⁴ +4x² +1=0

a,b,c,d are roots

find value of a⁴ + b⁴ +c⁴ +d⁴

^{1111----------(35) times}

^{is this divisible by 3,or 11}

ziauddin75

is there no one to solve on goiit

sboosy

ankitagg

is answer-1/4

pardesi

@sboosy i beleive that question was his signature
anyways
just complete the squares by adding 4x^{2} to both sides
this gives
(4x^{2}+1)^{2}=4x^{2}
so
u have two quadratics
4x^{2}+1-2x=0 roots a,b
4x^{2}+1+2x roots c,d
use them to get a^{4}+b^{4}
and c^{4}+d^{4} seperately and add them

varshavallig

11111-----35 times is not divisible by both.
sum=35 not div by 3
35 is odd,so sum of alternate nos is 17,18 which r not equal.so not div by 11.
!!!!!!!!!!!!!!!!!