Question

N(n+8)=273 x(x+6)=112​

Answer 1

Ответ:

Объяснение:

n(n+8)=273

n²+8n-273=0

Δ=1156  ; √Δ=34

n1=(-8-34)/2=-21

n2=(-8+34)/2=13

x(x+6)=112​

x²+6x-112=0

Δ=484   ; √Δ=22

x1=(-6-22)/2=-14

x2=(-6+22)/2=8

Answer 2

To solve the system of equations:

1. N(n + 8) = 273
2. x(x + 6) = 112

Let's start with the second equation:

2. x(x + 6) = 112

Expand the left side:

x^2 + 6x = 112

Now, move everything to one side to set the equation equal to zero:

x^2 + 6x - 112 = 0

We can factor this quadratic equation:

(x + 14)(x - 8) = 0

Now, set each factor equal to zero and solve for x:

1. x + 14 = 0 x = -14

2. x - 8 = 0 x = 8

So, there are two possible values for x: x = -14 and x = 8.

Now, let's use these values to solve the first equation:

1. N(n + 8) = 273

For x = -14: N(-14 + 8) = N(-6) = -6N

For x = 8: N(8 + 8) = N(16) = 16N

Now, we need to check if either of these values of N satisfies the equation:

1. -6N = 273 N = 273 / -6 N = -45.5

2. 16N = 273 N = 273 / 16 N = 17.0625

So, the solutions to the system of equations are:

For x = -14: N = -45.5 For x = 8: N = 17.0625

Therefore, the solutions to the system of equations are N = -45.5 and N = 17.0625, corresponding to the two values of x, -14 and 8, respectively.