Math Olympiad | A Nice Radical Problem |

Math Olympiad | A Nice Radical Problem | #algebra #mathslearning
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[@mrinaldas9614]

(1-×)^4=82-(x+1)^4 ,( 1-×)^4+(1+x)^4=82
Expand polynomials and add to get as shown in c❤omment p

[@bhaskarsinghal6527]

Only x=-2 satisfied the equation not x=2

[@prollysine]

we get , x^4+6x^2-40=0 , let u=x^2 , u^2=x^4 , u^2+6u-40=0 , u=(-6 |+/-| sqrt(36+160))/2 , u= -3 +7 , -3-7 , u= 4 , -10 .
x= |+/-| sqrt(u) , x= 2 , -2 , |+/-| i*sqrt(10) , test x=2 , 2+sqrt((82-(2+1)^4)^(1/4)) , -> 3 , not a solu. , x= -2 , -> -2+3=1 , same , OK ,
solu. , x= -2 ,