Question

1)-0,7(-10)⁴-8•(-10)²-26= 2)(√32-3)² 3)x²+4x=21

Answer 1

1) -0,7(-10)⁴-8•(-10)²-26=(-10)²(-0,7(-10)²-8)-26=100*(-70-8)-26=100*(-78)-26=-780-26= -806

2)(√32-3)²=32-6√32+9=41 - 6√32

3)x²+4x=21

x²+4x-21=0

D=16+84=100

√D=10

x1=(-4+10)/2=6/2=3

x2=(-4-10)/2= -14/2= -7

Answer 2

Let's solve each of these equations step by step:

1. -0.7(-10)⁴ - 8 * (-10)² - 26:

First, calculate -10⁴:

-10⁴ = 10,000

Now, calculate -10²:

-10² = 100

Now, plug these values into the equation:

-0.7 * 10,000 - 8 * 100 - 26

Now, perform the multiplications and subtractions:

-7,000 - 800 - 26

Now, add the numbers:

-7,000 - 800 - 26 = -7,826

So, the solution to the first equation is -7,826.

2. (√32 - 3)²:

First, calculate the square root of 32:

√32 ≈ 5.65685 (rounded to 5 decimal places)

Now, subtract 3 from the result:

5.65685 - 3 ≈ 2.65685 (rounded to 5 decimal places)

Now, square this result:

(2.65685)² ≈ 7.05081 (rounded to 5 decimal places)

So, the solution to the second equation is approximately 7.05081.

3. x² + 4x = 21:

To solve this quadratic equation, let's first set it equal to zero:

x² + 4x - 21 = 0

Now, we can solve for x using the quadratic formula:

x = (-b ± √(b² - 4ac)) / (2a)

In this equation, a = 1, b = 4, and c = -21.

x = (-4 ± √(4² - 4 * 1 * (-21))) / (2 * 1)

Now, calculate the discriminant (the value inside the square root):

Discriminant = 4² - 4 * 1 * (-21) = 16 + 84 = 100

Now, continue solving for x:

x = (-4 ± √100) / 2

x = (-4 ± 10) / 2

Now, calculate both solutions:

1. x = (-4 + 10) / 2 = 6 / 2 = 3
2. x = (-4 - 10) / 2 = -14 / 2 = -7

So, the solutions to the third equation are x = 3 and x = -7.