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Question Number 145019 by mathdanisur last updated on 01/Jul/21

Solve the equation: y+1=x^6 −9x^4 +6x^2 ; x;y∈P

Solvetheequation:y+1=x6−9x4+6x2;x;y∈P

Answered by Rasheed.Sindhi last updated on 01/Jul/21

y=x^6 −9x^4 +6x^2 −1 ; x;y∈P y=(x^3 −3x^2 +1)(x^3 +3x^2 −1) a) x^3 −3x^2 +1=1 ∧ x^3 +3x^2 −1=y OR b)x^3 −3x^2 +1=y ∧ x^3 +3x^2 −1=1 a) x^3 −3x^2 =0 ∧ x^3 +3x^2 −1=y x^2 (x−3)=0 ∧ x^3 +3x^2 −1=y x=3 ∧ (3)^3 +3(3)^2 −1=y x=3 ∧ y=53 b) x^3 +3x^2 −1=1 ∧ x^3 −3x^2 +1=y x^3 +3x^2 −2=0 ∧ x^3 −3x^2 +1=y No prime x ∧ No prime y

y=x6−9x4+6x2−1;x;y∈Py=(x3−3x2+1)(x3+3x2−1)a)x3−3x2+1=1∧x3+3x2−1=yORb)x3−3x2+1=y∧x3+3x2−1=1a)x3−3x2=0∧x3+3x2−1=yx2(x−3)=0∧x3+3x2−1=yx=3∧(3)3+3(3)2−1=yx=3∧y=53b)x3+3x2−1=1∧x3−3x2+1=yx3+3x2−2=0∧x3−3x2+1=yNoprimex∧Noprimey

Commented by mathdanisur last updated on 01/Jul/21

a lot cool Sir thankyou

alotcoolSirthankyou

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