The trichotomy law is essentially the law for ordering. Given any two real numbers, x and y, eitherx < y, orx = y, orx > y.
3X = x2 - 2xsubtract 3X from each sideX2 - 5X = 0factor out an XX(X - 5) = 0=========X = 0--------orX = 5--------
X2 + 3X = 0X(X + 3) = 0--------------------X is the greatest common factorso,X = 0----------orX = - 3----------- assuming you might want to solve this type of problem some day
Let the two numbers be x and y.Then;x + y = 100 -----(1)xy=25 -----(2)or x=25/yputting x=25/y in the first equation we get:25/y + y =10025 + y2 =100yy2 - 100y + 25 = 0x = 50 - 15sqrt(11) ; y = 50+15sqrt(11)orx = 50 + 15sqrt(11); y = 50 - 15sqrt(11)
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The trichotomy law is essentially the law for ordering. Given any two real numbers, x and y, eitherx < y, orx = y, orx > y.
3x + 5x = 348x = 34x = 34/8x = 17/4 orx = 4.25
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Two solutions:x = 5 and y = 6, orx = 6 and y = 5.
3X = x2 - 2xsubtract 3X from each sideX2 - 5X = 0factor out an XX(X - 5) = 0=========X = 0--------orX = 5--------
('x' times 'x') plus 'x' = 30x2 + x - 30 = 0(x + 6) (x - 5) = 0x = -6and/orx = 5
X2 + 3X = 0X(X + 3) = 0--------------------X is the greatest common factorso,X = 0----------orX = - 3----------- assuming you might want to solve this type of problem some day
1. If the question is only to factor this expression:x^2 + 5x = x(x + 5)2. If the question is to solve the equation x^2 + 5x = 0:x^2 + 5x = 0 factor it;x(x + 5) = 0x = 0 orx + 5 =0 subtract 5 to both sides;x = - 5
6x2 + 7x = 56x2 + 7x - 5 = 0x =[ -7 ± √[72 - 4(6)(-5)] ]/2(6)x = [-7 ± √(49 + 120)]/12x = (-7 ± √ 169)/12x = (-7 ± 13)/12x = (-7 + 13)/12 or x = (-7 - 13)/12x = 6/12 = 1/2 orx = -20/12 = - 5/3
Let the two numbers be x and y.Then;x + y = 100 -----(1)xy=25 -----(2)or x=25/yputting x=25/y in the first equation we get:25/y + y =10025 + y2 =100yy2 - 100y + 25 = 0x = 50 - 15sqrt(11) ; y = 50+15sqrt(11)orx = 50 + 15sqrt(11); y = 50 - 15sqrt(11)