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Solve-x-x-1-2-x-x-1-2-6-

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Question Number 217911 by Rasheed.Sindhi last updated on 23/Mar/25
Solve ((x/(x−1)))^2 +((x/(x+1)))^2 =6
Solve(xx−1)2+(xx+1)2=6
Answered by Rasheed.Sindhi last updated on 23/Mar/25
((x/(x−1)))^2 +((x/(x+1)))^2 =6 ((x/(x−1)))^2 −1+((x/(x+1)))^2 −1=4 ((x/(x−1))−1)((x/(x−1))+1)+((x/(x+1))−1)((x/(x+1))+1)=4 (1/(x−1))∙((2x−1)/(x−1))+((−1)/(x+1))∙((2x+1)/(x+1))=4 (((2x−1)(x+1)^2 −(2x+1)(x−1)^2 )/((x^2 −1)^2 ))=4 (2x−1)(x^2 +2x+1)−(2x+1)(x^2 −2x+1)=4(x^4 −2x^2 +1) ▶2x^3 +4x^2 +2x−x^2 −2x−1 −2x^3 +4x^2 −2x−x^2 +2x−1 =4x^4 −8x^2 +4 ▶3x^2 −1 +3x^2 −1 =4x^4 −8x^2 +4 ▶6x^2 −2=4x^4 −8x^2 +4 ▶ 4x^4 −14x^2 +6=0 ▶2x^4 −7x^2 +3=0 ▶2x^4 −6x^2 −x^2 +3=0 ▶2x^2 (x^2 −3)−(x^2 −3) ▶(x^2 −3)(2x^2 −1) ▶x=±(√3) ∨ x=±(1/( (√2)))=((±(√2) )/2) ▶x∈{(√3) ,−(√3) , ((√2)/2) ,−((√2)/2)}
(xx−1)2+(xx+1)2=6(xx−1)2−1+(xx+1)2−1=4(xx−1−1)(xx−1+1)+(xx+1−1)(xx+1+1)=41x−1⋅2x−1x−1+−1x+1⋅2x+1x+1=4(2x−1)(x+1)2−(2x+1)(x−1)2(x2−1)2=4(2x−1)(x2+2x+1)−(2x+1)(x2−2x+1)=4(x4−2x2+1)▸2x3+4x2+2x−x2−2x−1−2x3+4x2−2x−x2+2x−1=4x4−8x2+4▸3x2−1+3x2−1=4x4−8x2+4▸6x2−2=4x4−8x2+4▸4x4−14x2+6=0▸2x4−7x2+3=0▸2x4−6x2−x2+3=0▸2x2(x2−3)−(x2−3)▸(x2−3)(2x2−1)▸x=±3∨x=±12=±22▸x∈{3,−3,22,−22}
Answered by Rasheed.Sindhi last updated on 23/Mar/25
x^2 (x+1)^2 +x^2 (x−1)^2 =6(x^2 −1)^2 x^2 {(x^2 +2x+1)+(x^2 −2x+1)}=6(x^4 −2x^2 +1) x^2 (2x^2 +2)=6x^4 −12x^2 +6 2x^4 +2x^2 =6x^4 −12x^2 +6 4x^4 −14x^2 +6=0 2x^4 −7x^2 +3=0 2x^4 −6x^2 −x^2 +3=0 2x^2 (x^2 −3)−(x^2 −3)=0 (x^2 −3)(2x^2 −1)=0 x=±(√3) ∨ x=±((√2)/2)
x2(x+1)2+x2(x−1)2=6(x2−1)2x2{(x2+2x+1)+(x2−2x+1)}=6(x4−2x2+1)x2(2x2+2)=6x4−12x2+62x4+2x2=6x4−12x2+64x4−14x2+6=02x4−7x2+3=02x4−6x2−x2+3=02x2(x2−3)−(x2−3)=0(x2−3)(2x2−1)=0x=±3∨x=±22

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