2x2+7/x1
The inverse of a number is 1 divided by that number. So the inverse of x3 + 1 is 1/(x3 + 1).
notation: natural numbers = 0,1, 2, 3, 4, 5, ....., (some define it without the zero, though) <= means smaller than or equal to, {} is set notation and means a set of numbers : (such that) then some condition. For example {x: x is not a duck} is the set of all things not a duck. Our goal is to prove that there are 21 different times. let x1 = hours, x2 = tens of minutes, x3 = minutes. We are going to prove the statement about the set {x1, x2,x3: 1<=x1 <= 12, 0<= x2<=5, 0<=x3 <= 59, x1 + x2 + x3 = 6}. It will be taken by assumption that this set is the set of digital clock combinations that add up to 6. So then, we must prove that there are unique 21 elements in the set {x1 + x2 + x3 : 1<= x1 <= 12, 0<= x2<=5, 0<=x3 <= 59, x1 + x2 + x3 = 6}. {x1 , x2 , x3 : 1<= x1 <= 12, 0<= x2<=5, 0<=x3 <= 59, x1 + x2 + x3 = 6} = {x1 , x2 , x3 : 1<= x1 <= 6, 0<= x2<=5, 0<=x3 <= 5, x1 + x2 + x3 = 6} because x3<=6, and because if x1 >=1, then x2 + x3 <=5, and x3, x2 >= 0 , so surely x3, x2 <= x5. Either x1 = 1, 2, 3, 4, 5, or 6. Next, x1 + x2 + x3 = 6, so x2 + x3 = 6 - x1. There are n+1 natural numbers between 0 and n (I'm being lazy and not proving this, but the proof would be so much longer if I proved it), and since 0 <= x2 <= 5 <= 6-x1, there are at most 6-x1+1 values of x2 for each value of x1. When x1 = 1, there are a maximum of 6, when x1 = 2, there are 6-2+1 = 5, when x1 = 3, there are 6-3+1 = 4, when x1 = 3, there are 3, then 2, and then 1. Summing this up gives us a maximum of 21. So it is at most 21 and at least 21, so exactly 21.
== == Suppose f(x) = x3 + 3x2 - 2x + 7 divisor is x + 1 = x - (-1); so rem = f(-1) = 11
That depends on whether or not 2x is a plus or a minus
x3+3x2+6x+1 divided by x+1 Quotient: x2+2x+4 Remaider: -3
By x3 I assume that you mean x3. In which case f(x)=x3-2x+1, and f'(x)=3x2-2. Therefore our iteration formula is: xn+1=xn- (xn3-2xn+1)/(3xn2-2) Starting with x0=0 we get: x1=0.5 x2=0.6 x3=0.617391304 x4=0.618033095 x5=0.618033988 x6=0.618033988 Starting with x0=0.9 we get: x1=1.065116279 x2=1.009457333 x3=1.000255451 x4=1.000000195 x5=1 x6=1 Starting with x0=-1.5 we get: x1=-1.631578947 x2=-1.618183589 x3=-1.618034007 x4=-1.618033989 x5=-1.618033989 The 3 real roots to f(x) are x=-1.618033989, x=0.618033988, and x=1
Dividend: 4x4-x3+17x2+11x+4 Divisor: 4x+3 Quotient: x3-x2+5x-1 Remainder: 7
x3+3x2+3x+2 divided by x+2 equals x2+x+1
monsters(19) 1.prime material dragon x2 2.the creator x2 3.cyber dragon x1 4.freed the brave wanderer x2 5.zaborg the thunder monarch x3 6.copycat x1 7.reflect bounder x1 8.skelengel x2 9.morphing jar x1 10.marshmallon x1 11.d.d. warrior lady x1 12.the creator incarnate x2 spelles(17) 1.card of safe return x3 2.heavy storm x1 3.monster reborn x1 4.reinforscment of the army x3 5.enemy controller x1 6.fissure x1 7.smashing ground x1 8.mystical space typhoon x1 9.foolish burrial x2 10.shrink x2 11.lightning vortex x1 12.monster reincarnation x1 traps(5) 1.solmen judgment x3 2.mirror force x1 3.torrential tribute x1
3
(x + 4) / (x3 - 11x + 20) = (x + 4) / (x2 + 4x - 5)(x + 4) = 1 / (x2 + 4x - 5) = 1 / (x + 5)(x - 1), where x ≠ -4