Question Number 113997 by Aina Samuel Temidayo last updated on 16/Sep/20

Answered by bobhans last updated on 16/Sep/20

consider : (√2) +(2)^(1/4)  +1 = ((2)^(1/4) )^2 +1.((2)^(1/4) )+1^2  = ((((2)^(1/4) )^3 −1^3 )/( (2)^(1/4) −1))  then (7/(((2)^(1/4) )^2 +(2)^(1/4) +1)) = ((7((2)^(1/4) −1))/( ((2^3 )^(1/4) )−1))

Answered by 1549442205PVT last updated on 16/Sep/20

(7/(2^(1/2) +2^(1/4) +1))=A+B.2^(1/4) +C.2^(1/2) +D.2^(3/4)   ⇔(2^(1/2) +2^(1/4) +1)(A+B.2^(1/4) +C.2^(1/2) +D.2^(3/4) )=7  ⇔A.2^(1/2) +A.2^(1/4) +A+B.2^(3/4) +B.2^(1/2) +B.2^(1/4)   +2C+C.2^(3/4) +C.2^(1/2) +D.2^(5/4) +D.2+D.2^(3/3)   =(A+2C+2D)+(A+B+C).2^(1/2)   +(A+B+2D).2^(1/4) +(B+C+D)^(3/4) =7  ⇔ { ((A+2C+2D=7(sinceD. 2^(5/4) =2D.2^(1/4) ))),((A+B+C=0)),((A+B+2D=0)),((B+C+D=0)) :}  Solve above system we get:  A=1,B=−3,C=2,D=1  Hence,there are three true options  in available answer