Menu Close

solve-x-3-3x-1-0-




Question Number 82582 by M±th+et£s last updated on 22/Feb/20
solve  x^3 −3x+1=0
solvex33x+1=0
Commented by mr W last updated on 23/Feb/20
x^3 +3(−1)x+2((1/2))=0  p=−1  q=(1/2)  Δ=p^3 +q^2 =−1+(1/4)=−(3/4)<0  ⇒three real roots  x=2(√(−p)) sin ((1/3)sin^(−1) (q/( (√(−p^3 ))))+((2kπ)/3))  =2 sin ((1/3)sin^(−1) (1/2)+((2kπ)/3))  =2 sin ((π/(18))+((2kπ)/3))  (k=0,1,2)  x_1 =2 sin ((π/(18)))=0.347296  x_2 =2 sin ((π/(18))+((2π)/3))=1.532089  x_3 =2 sin ((π/(18))+((4π)/3))=−1.879385
x3+3(1)x+2(12)=0p=1q=12Δ=p3+q2=1+14=34<0threerealrootsx=2psin(13sin1qp3+2kπ3)=2sin(13sin112+2kπ3)=2sin(π18+2kπ3)(k=0,1,2)x1=2sin(π18)=0.347296x2=2sin(π18+2π3)=1.532089x3=2sin(π18+4π3)=1.879385
Commented by M±th+et£s last updated on 23/Feb/20
thank you sir nice solution
thankyousirnicesolution

Leave a Reply

Your email address will not be published. Required fields are marked *