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x-2-2x-3-2-3x-2-6x-9-0-What-is-the-value-of-x-

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Question Number 9884 by Joel575 last updated on 12/Jan/17
(x^2 −2x+3)^2 + (3x^2 −6x−9) = 0 What is the value of x ?
(x2−2x+3)2+(3x2−6x−9)=0Whatisthevalueofx?
Answered by sandy_suhendra last updated on 12/Jan/17
(x^2 −2x+3)^2 +3(x^2 −2x+3)−18=0 let x^2 −2x+3=a a^2 +3a−18=0 (a+6)(a−3)=0 (1) a=−6 x^2 −2x+3=−6 x^2 −2x+9=0 x_(1,2) =((2±(√(4−36)))/2) ⇒ x=imaginary (2) a=3 x^2 −2x+3=3 x^2 −2x=0 x(x−2)=0 x_1 =0 or x_2 =2
(x2−2x+3)2+3(x2−2x+3)−18=0letx2−2x+3=aa2+3a−18=0(a+6)(a−3)=0(1)a=−6x2−2x+3=−6x2−2x+9=0x1,2=2±4−362⇒x=imaginary(2)a=3x2−2x+3=3x2−2x=0x(x−2)=0x1=0orx2=2
Commented by ridwan balatif last updated on 12/Jan/17
i think it should be x^2 −2x+3=−6 not x^2 −2x+3=6
ithinkitshouldbex2−2x+3=−6notx2−2x+3=6
Commented by sandy_suhendra last updated on 12/Jan/17
thank′s, I have fixed it
thank′s,Ihavefixedit
Commented by Joel575 last updated on 14/Jan/17
thank you very much
thankyouverymuch
Answered by ridwan balatif last updated on 12/Jan/17
(x^2 −2x+3)^2 +3(x^2 −2x−3)=0 {(x^2 −2x)+3}^2 +3{(x^2 −2x)−3}=0 (x^2 −2x)^2 +6(x^2 −2x)+9+3(x^2 −2x)−9=0 (x^2 −2x)^2 +9(x^2 −2x)=0 (x^2 −2x)((x^2 −2x)+9)=0 (I).x^2 −2x=0 x(x−2)=0 x=0 ∨ x=2 (II) x^2 −2x+9=0 D=b^2 −4ac =−32 (IMPOSSIBLE)
(x2−2x+3)2+3(x2−2x−3)=0{(x2−2x)+3}2+3{(x2−2x)−3}=0(x2−2x)2+6(x2−2x)+9+3(x2−2x)−9=0(x2−2x)2+9(x2−2x)=0(x2−2x)((x2−2x)+9)=0(I).x2−2x=0x(x−2)=0x=0∨x=2(II)x2−2x+9=0D=b2−4ac=−32(IMPOSSIBLE)

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