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n200080 [17]
2 years ago
10

From the quadratic equation 3x² + X - 5 = 0, find alpha square plus beta square​

Mathematics
1 answer:
timama [110]2 years ago
4 0

Answer:

  α² +β² = 3 4/9

Step-by-step explanation:

Assuming α and β are solutions to the equation, it can be factored as ...

  (x -α)(x -β) = 0

Expanding this, we get ...

  x² -(α +β)x +αβ = 0

Dividing the original equation by 3, we find ...

  x² +(1/3)x -5/3 ≡ x² -(α+β)x +αβ   ⇒   (α+β) = -1/3, αβ = -5/3

We know that the square (α+β)² can be expanded to ...

  (α +β)² = α² +β² +2αβ

  α² +β² = (α +β)² -2αβ . . . . . . subtract 2αβ

Substituting the values for (α+β) and αβ, we find the desired expression is ...

  α² +β² = (-1/3)² -2(-5/3) = 1/9 +10/3 = 31/9

  α² +β² = 3 4/9

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3 years ago
The length of a rectangle is 4 cm longer than its width. If the perimeter of the rectangle is 44 cm, find its area.​
adell [148]
Length: w+4
Width:w
Perimeter:44
Area: L times w
P=44
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5 0
4 years ago
What is the value of x, the acid concentration of the first solution?
bezimeni [28]

Answer:

A) 0.05

Step-by-step explanation:

Let's summarize into an equation the information we can get from that table.

We have 4 liters of an acid of an unknown concentration, let's call it (4x).

We have 10 liters of an acid with known concentration of 0.40.

And we have a total of 14 liters overall with a concentration of 0.3o.

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6 0
3 years ago
Read 2 more answers
Can someone please help me with #3?
kap26 [50]

Answer:


Step-by-step explanation:

First, make sure you know which section of the number line you want as 1 and 2. Next, put 0.25 not right at 0 but very close, then put 0.75 farther but not too much from 0.25. Then for the decimal 1.99 put that very close to where you marked the 2 but, not on the 2. Finally, put 2.03  very close to 2 but not exactly on the 2. Also, make sure that the number line is marked evenly.

7 0
3 years ago
Solve for x<br> Please help
Igoryamba

Answer:

3. A; 4. C; 5. D; 6. D

Step-by-step explanation:

3. By Pythagorean theorem, x^2=100-64=36, x=6

4. By Pythagorean theorem, x^2=81-36=25, x=5

5. Since the triangle is an isosceles, the other side is 4, so the hypotenuse is 4\sqrt{2}. (the ratio is 1:1:\sqrt{2} by Pythagorean theorem)

6. Like Question #5, the ratio is 1:1:\sqrt{2} since it is an isosceles triangle, the leg is 8.

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3 years ago
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