Question

P(x-3) + P(x+1) = 2-10x+16, P(x) -?

Answer 1

Объяснение:

В приложении к ответу

Answer 2

Ответ:

P(x)=x²-3x

Объяснение:

Пусть P(x)=ax²+bx+c, тогда

P(x-3)=a(x-3)²+b(x-3)+c

P(x+1)=a(x+1)²+b(x+1)+c

P(x-3)+P(x+1)=2x²-10x+16

a(x-3)²+b(x-3)+c+a(x+1)²+b(x+1)+c=2x²-10x+16

a(x²-6x+9)+bx-3b+2c+a(x²+2x+1)+bx+b=2x²-10x+16

ax²-6ax+9a+bx-3b+2c+ax²+2ax+a+bx+b=2x²-10x+16

2ax²+(-6a+b+2a+b)x+9a-3b+2c+a+b=2x²-10x+16

2ax²+(2b-4a)x+10a-2b+2c=2x²-10x+16

1) 2a=2

a=1

2) 2b-4a=-10

2b-4=-10

2b=-6

b=-3

3) 10a-2b+2c=16

10+6+2c=16

2c=0

c=0

P(x)=x²-3x

Answer 3

To find the expression for P(x), you can start by simplifying the given equation:

P(x - 3) + P(x + 1) = 2 - 10x + 16

Now, let's isolate one of the P(x) terms. You can do this by moving P(x + 1) to the other side of the equation:

P(x - 3) = 2 - 10x + 16 - P(x + 1)

Now, you can manipulate this equation to solve for P(x). Start by moving P(x + 1) to the left side of the equation:

P(x - 3) + P(x + 1) + P(x + 1) = 2 - 10x + 16 - P(x + 1) + P(x + 1)

Simplify the equation:

P(x - 3) + 2P(x + 1) = 2 - 10x + 16

Now, isolate the P(x) term on the left side by subtracting (2P(x + 1)) from both sides:

P(x - 3) = 2 - 10x + 16 - 2P(x + 1)

P(x - 3) = 18 - 10x - 2P(x + 1)

Now, you can express P(x) in terms of P(x + 1) as follows:

P(x) = 18 - 10x - 2P(x + 1) + P(x - 3)

This expression represents P(x) in terms of P(x + 1) and P(x - 3).