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3 years ago

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

Mathematics

1 answer:

Andrej [43]3 years ago

6 0

Answer:

x = -1 and x = 5

Step-by-step explanation:

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

(x – 3)² + 2(x – 3) -8 = 0 -------------------------------------------------------(1)

To solve this problem, we will follow the steps below;

let u = x-3

we will replace x-3 by u in the given equation:

(x – 3)² + 2(x – 3) -8 = 0

u² + 2u -8 = 0 ----------------------------------------------------------- --------------(2)

We will now solve the above quadratic equation

find two numbers such that its product gives -8 and its sum gives 2

The two numbers are 4 and -2

That is; 4×-2 = -8 and 4+(-2) = 2

we will replace 2u by (4u -2u) in equation (2)

u² + 2u -8 = 0

u² + 4u - 2u -8 = 0

u(u+4) -2(u+4) = 0

(u+4)(u-2) = 0

Either u + 4 = 0

u = -4

u-2 = 0

u = 2

Either u = -4 or u = 2

But u = x-3

x = u +3

when u = -4

x = u + 3

x = -4 + 3

x=-1

when u = 2

x = u + 3

x = 2 + 3

x=5

Therefore, x = -1 and x =5

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3 years ago

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3 years ago

1.How much taller Porter is than Henry, given that Porter is n inches tall and Henry is m inches tall. 2.How many times as tall

EleoNora [17]

Answer:

Porter is $n-m$ inches taller than Henry.

Porter is $\frac{n}{m}$ times taller than henry.

Step-by-step explanation:

The difference in height can be found using subtraction.

Since Porter is taller than Henry, we'll subtract away Henry's height from Porter's height. This will leave us with only the difference between the heights.

n = Porter's height

m = Henry's height

Difference in height is thus:

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Answer: Porter is $n-m$ inches taller than Henry.

To find out how many times taller Porter is than Henry, we can use division.

An example: if Porter was 200cm, and Henry was 100cm, Porter is obviously 2 times as tall.

If we divide Porter's height by Henry's height...

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Using our values, n and m, we'll divide n by m.

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Alex17521 [72]

G(f(12))
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