Answer: 48,60
Step-by-step explanation:
4x+5x=108
9x=108
x=108/9=12
12•4=48
12•5=60
I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take

, so that

and we're left with the ODE linear in

:

Now suppose

has a power series expansion



Then the ODE can be written as


![\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%5Cge2%7D%5Cbigg%5Bn%28n-1%29a_n-%28n-1%29a_%7Bn-1%7D%5Cbigg%5Dx%5E%7Bn-2%7D%3D0)
All the coefficients of the series vanish, and setting

in the power series forms for

and

tell us that

and

, so we get the recurrence

We can solve explicitly for

quite easily:

and so on. Continuing in this way we end up with

so that the solution to the ODE is

We also require the solution to satisfy

, which we can do easily by adding and subtracting a constant as needed:
So the two numbers can be represented as x and y
so x is first and y is second
y=2(x)-8
so y=2x-8
IF THEY ARE CONSECUTIVE
If they are consecutive numbers then
x+1=y
subtitute
x+1=2x-8
subtract x from both sides
1=x-8
add 8 to both sides and get
9=x
put it into the equation and get
y=2(9)-8
y=18-8
y=10
so x=9
y=10
IF X AND Y ARE CONSECUTIVE INTEGERS (1,2,3,4 not 2.3 or 1,3,5,8)
Answer:
- x² - 8x + 12
- x³ + 2x² - 15x - 36
- x³ -2x² - 15x
Step-by-step explanation:
#1) Find the polynomial with roots at 2 and 6
-
(x -2)(x - 6) = x² - 8x + 12
#2) Find the polynomial with a double root at -3 and another root at 4
-
(x+3)(x+3)(x-4) = (x²+6x+9)(x-4) = x³ + 2x² - 15x - 36
#3) Find the polynomial with roots 0, -3 and 5
- (x -0)(x+3)(x-5) = x(x²-2x - 15) = x³ -2x² - 15x