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Question Number 131605 by physicstutes last updated on 06/Feb/21
solve the equation m^4 −7m^3 + 14m^2 −7m + 1 = 0
solvetheequationm4−7m3+14m2−7m+1=0
Answered by malwan last updated on 06/Feb/21
m^4 +(−3m^3 −4m^3 ) +(m^2 +12m^2 +m^2 ) +(−4m−3m)+1=0 ⇒(m^4 −3m^2 +m^2 ) +(−4m^3 +12m^2 −4m) +(m^2 −3m+1)=0 ⇒m^2 (m^2 −3m+1) −4m(m^2 −3m+1) +(m^2 −3m+1)=0 ⇒(m^2 −3m+1)(m^2 −4m+1)=0 m^2 −3m+1=0 ⇒m=((3±(√(9−4)))/2) = ((3±(√5))/2) or m^2 −4m+1=0 ⇒m=((4±(√(16−4)))/2) = 2±(√3)
m4+(−3m3−4m3)+(m2+12m2+m2)+(−4m−3m)+1=0⇒(m4−3m2+m2)+(−4m3+12m2−4m)+(m2−3m+1)=0⇒m2(m2−3m+1)−4m(m2−3m+1)+(m2−3m+1)=0⇒(m2−3m+1)(m2−4m+1)=0m2−3m+1=0⇒m=3±9−42=3±52orm2−4m+1=0⇒m=4±16−42=2±3
Commented by physicstutes last updated on 06/Feb/21
thats awsome sir
thatsawsomesir
Commented by malwan last updated on 06/Feb/21
thanks
thanks
Answered by EDWIN88 last updated on 06/Feb/21
(1)(m^2 +km+1)(m^2 +ℓm+1)=m^4 −7m^3 +14m^2 −7m+1 ⇒m^4 +(ℓ+k)m^3 +(2+kℓ)m^2 +(k+ℓ)m+1= m^4 −7m^3 +14m^2 −7m+1 ⇒ { ((k+ℓ=−7⇒k=−7−ℓ)),((2+kℓ=14;kℓ=12)) :} ⇒ℓ(−7−ℓ)=12; ℓ^2 +7ℓ+12=0 → { ((ℓ=−3)),((k=−4)) :} then ⇔ (m^2 −3m+1)(m^2 −4m+1)=0 ⇔[(m−(3/2))^2 −(5/4) ] [(m−2)^2 −3 ] = 0 ⇔ m = { (((3/2)±((√5)/2))),((2± (√3))) :} .
(1)(m2+km+1)(m2+ℓm+1)=m4−7m3+14m2−7m+1⇒m4+(ℓ+k)m3+(2+kℓ)m2+(k+ℓ)m+1=m4−7m3+14m2−7m+1⇒{k+ℓ=−7⇒k=−7−ℓ2+kℓ=14;kℓ=12⇒ℓ(−7−ℓ)=12;ℓ2+7ℓ+12=0→{ℓ=−3k=−4then⇔(m2−3m+1)(m2−4m+1)=0⇔[(m−32)2−54][(m−2)2−3]=0⇔m={32±522±3.

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