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Alexxandr [17]
3 years ago
5

What are the solutions of the equation (x-3)2 + 2(x – 3) - 8= 0? Use u substitution to solve.

Mathematics
2 answers:
astraxan [27]3 years ago
5 0

Answer:

x = - 1 and x = 5

Step-by-step explanation:

Given

(x - 3)² + 2(x - 3) - 8 = 0

Let u = x - 3, then

u² + 2u - 8 = 0 ← solve for u

(u + 4)(u - 2) = 0 ← in factored form

Equate each factor to zero and solve for u

u + 4 = 0 ⇒ u = - 4

u - 2 = 0 ⇒ u = 2

Convert back to x, that is

x - 3 = - 4 ( add 3 to both sides ) ⇒ x = - 1

x - 3 = 2 ( add 3 to both sides ) ⇒ x = 5

earnstyle [38]3 years ago
3 0

Answer:  The correct option is

(B) x = -1 and x = 5.

Step-by-step explanation: We are given the following equation :

(x-3)^2+2(x-3)-8=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)

We are to find the solutions of the above equation.

Let u= (x-3).

Then, from equation (i), we have  

u^2+2u-8=0\\\\\Rightarrow u^2+4u-2u-8=0\\\\\Rightarrow u(u+4)-2(u+4)=0\\\\\Rightarrow (u-2)(u+4)=0\\\\\Rightarrow u-2=0,~~~~~~~~~~~~u+4=0\\\\\Rightarrow x-3-2=0,~~~\Rightarrow x-3+4=0\\\\\Rightarrow x=5,~x=-1.

Thus, the required solution is x = -1 and x = 5.

Option (B) is CORRECT.

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Answer:

The intersection point  of the given lines is  (1,1).

Step-by-step explanation:

Here, the given equations are:

y  =  - 2 x +  3

y  =  x​

Substitute y = x in  the first equation,

y   = -2 x  +  3 becomes      y =  -2 (y)  + 3

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or, 3 y = 3  ⇒  y = 3/3 = 1

⇒  y =  1

Now, as x =  y ⇒ x =   1

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The intercepts of the graph are:

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y-axis interception: \left(0,\:-9\right).

See the graph of the function f(x)=x^3+x^2-9x-9  in the attached image.

<h3>Constructing a graph</h3>

For constructing a graph we have the following steps:

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For this exercise, for example, we can define a range -4<x<4.  In others words, the values of x will be in this interval.

  • Determine the points

Replace these x-values in the given equation. For example:

When x=-4, we will have: \left(-4\right)^3+\left(-4\right)^2-9\left(-4\right)-9=-21.  Do this for the all x-values of your ranges.

See the results for this step in the attached table.

  • Draw the graph

Mark the points <u>x</u> and<u> y</u> that you found in the last step. After that, connect the dots to draw the graph.

The attached image shows the graph for the given function.

<h3>Find the x- and y-intercepts</h3>

The intercepts are points that crosses the axes of your plot. From your graph is possible to see:

x-axis interception points (y=f(x)=0)  are: \left(-1,\:0\right),\:\left(-3,\:0\right),\:\left(3,\:0\right).

y-axis interception point (x=0) is: \left(0,\:-9\right).

Learn more about intercepts of the graph here:

brainly.com/question/4504979

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