˜A—§•û’öŽ® |
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[‰‰K1] [‰ð“š1] [Maple10]@ |
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[‰‰K2]@
¶—“IH‰–…‚ð‚P‚O‚O‚O‚‡ì‚肽‚¢B…‰½ƒOƒ‰ƒ€‚ÉH‰–‰½ƒOƒ‰ƒ€‚𬂺‚ê‚Îì‚ê‚é‚©H [‰ð“š2] |
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[‰‰K3] |
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[‰‰K4] ax+by=3, ax^2 +by^2=7, ax^3 +by^3=16, ax^4 +by^4=42 ‚ð‰ð‚«A‚»‚ÌŽž‚Ì ax^5 +by^5 ‚Ì’l‚ð‹‚ß‚æB [‰ð] [Maple10Žg—p] solve([ax+by=3,ax^2+by^2=7,ax^3+by^3=16,{y,a,b}) {y=(7x-16)/(3x-7),a=-1/(x(3x^2-14x+16)),b=((3x-7)^3)/((7x-16)(3x^2-14x+16))} solve(eval(ax^4+by^4=42,[y=(7x-16)/(3x-7),a=-1/(x(3x^2-14x+16)),b=((3x-7)^3)/((7x-16)(3x^2-14x+16))]),{x}) {x=-7+ã87},{x=-7-ã87} c:=-7+ã87;d:=-7-ã87 {x=-7+ã87} a:=factor(simplify(eval(-1/(x(3x^2-14x+16)),x=c))) a:=(49/76)+(457/6612)ã87 b:=factor(simplify(eval(((3x-7)^3)/((7x-16)(3x^2-14x+16)),x=c))) b:=(49/76)-(457/6612)ã87 y:=factor(simplify(eval((7x-16)/(3x-7),x=c))) y:=-7-ã87 {x=-7-ã87} a:=factor(simplify(eval(-1/(x(3x^2-14x+16)),x=d))) a:=(49/76)-(457/6612)ã87 b:=factor(simplify(eval(((3x-7)^3)/((7x-16)(3x^2-14x+16)),x=d))) b:=(49/76)+(457/6612)ã87 y:=factor(simplify(eval((7x-16)/(3x-7),x=d))) y:=-7+ã87 factor(eval(ax^5+by^5,[a=(49/76)+(457/6612)ã87,(49/76)-(457/6612)ã87,x=-7+ã87, y=-7-ã87])) 20 ˆÈã‚©‚ç (x,y,a,b)=(-7+ã87,-7-ã87,(4263+457ã87)/6612,(4263-457ã87)/6612), (-7-ã87,-7+ã87,(4263-457ã87)/6612,(4263+457ã87)/6612) ax^5+by^520 |
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[•Ê‰ð] ax+by=3, ax^2 +by^2=7, ax^3 +by^3=16, ax^4 +by^4=42 c(D) (ax+by)(x+y)=ax^2+by^2+xy(a+b) 3(x+y)=7+xy(a+b)@c(A) (ax^2+by^2)(x+y)=ax^3+by^3+xy(ax+by) 7(x+y)=16+3xy@c(B) (ax^3+by^3)(x+y)=ax^4+by^4+xy(ax^2+by^2) 16(x+y)=42+7xy@c(C) (B),(C)‚©‚ç x+y=-14, xy=-38@c(E) (A)‚É‘ã“ü a+b=49/38@c(F) x,y‚Í z^2+14z-38=‚Ì2ª x,y=-7}ã87@c(G) (F),(G)‚ð(D)‚É‘ã“ü -(7*49/38)+(a-b)ã87=3@c(H) (F),(H)‚©‚ç a,b=(49/76)}(457/6612)ã87@c(I) ‚Ü‚Æ‚ß‚Ä (a,b,x,y)=((49/76)+(457/6612)ã87,(49/76)-(457/6612)ã87,-7+ã87,-7-ã87) or ((49/76)-(457/6612)ã87,(49/76)+(457/6612)ã87,-7-ã87,-7+ã87) ax^5+by^5=(x+y)(ax^4+by^4)-xy(ax^3+by^3)=-14*42+38*16=20 |
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s—ñ‚ð—p‚¢‚½˜A—§•û’öŽ®‚̉ð–@ |
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[‰‰K1] A@= [ 1 2 ]@ @@ [ 1 1 ] [X] = A [x] ‚Æ‚¨‚‚Æ [Y] [y] [x] = A -1 [X] = [ -1 2 ] [X] [y] [Y] [ 1 -1] [Y] ‘‚«‰º‚·‚Æ x=-X+2Y, y=X-Y ‚±‚ê‚ðuy = xv‚É‘ã“ü‚µ‚Ä -X+2Y=X-Y Ë 3Y = 2X @ˆ Y = (2/3) X © (“š‚¦) |
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[‰‰K] ŽŸ‚̘A—§ˆêŽŸ•û’öŽ®‚ð‰ð‚«‚È‚³‚¢ 5x + 3y - 3z = 2 2x - y + z = 3 x + y + z = 6 [‰ð“š] ŒW”s—ñ‚Í [ 5 3 -3 ] A = [ 2 -1 1 ] , det A = -22, [ 1 1 1 ] [ -2 -6 0 ] [2 6 0 ] A -1 = [ -1 8 -11 ] / det A = [1 -8 11 ] /22 [ 3 -2 -11 ] [-3 2 11 ] ˜A—§ˆêŽŸ•û’öŽ®‚ð‘‚«Š·‚¦‚é‚Æ [x] [2] A [y] = [3] [z] [6] @ [x] [2] [ 2 6 0 ] [2] [1] ˆ [y] = A -1 [3] = [ 1 -8 11 ] [3]/22 = [2] [z] [6] [ -3 2 11 ] [6] [3] i“š‚¦j x=1, y=2, z=3 |
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