Question

Решить уравнение; (3х-2)^2+(1-3х)(3х+2)=36 x(x-2)(x-3)=8+x9x-2,5)^2 (6x-1)^2-(5x+2)(6x+5)=6(x-1)^2-37x (2x-1)(2x+1)=2(x-3)^2=x(2x-3) упростите выражение и найдите его значение (a-2b)^2-(2a-b)^2,если a=-2,b=-3 (a^2 -2)^2-(a^2-1)(a^2+2)+5(a-4)^2,если a=-0,125 (m-3)^2-(m-2)(m+2), если m=-2,5 (b^2-1)(b^2+1)-(b^2+2)^2,если b=-3

Answer 1

Вот ответ там несколько не получилось из за того что вы наверно не верно списали

Answer 2

To solve the equations, we'll start by solving each one step-by-step:

1. (3x-2)^2 + (1-3x)(3x+2) = 36

Expand the terms:

(9x^2 - 12x + 4) + (3x - 9x^2 - 4) = 36

Combine like terms:

-12x + 3x = 36

-9x = 36

Now, solve for x:

x = 36 / -9

x = -4

2. x(x-2)(x-3) = 8 + x(9x-2.5)^2

Expand the terms:

x^3 - 5x^2 + 6x = 8 + x(81x^2 - 45x + 6.25)

Distribute x:

x^3 - 5x^2 + 6x = 8 + 81x^3 - 45x^2 + 6.25x

Move all terms to one side:

x^3 - 5x^2 + 6x - 81x^3 + 45x^2 - 6.25x - 8 = 0

Combine like terms:

-80x^3 + 40x^2 - 0.25x - 8 = 0

Now, solving this cubic equation for x requires a more involved process. It's beyond simple algebraic manipulations. To get the exact values for x, you can use numerical methods, such as Newton-Raphson method or numerical solvers in software.

3. (6x-1)^2 - (5x+2)(6x+5) = 6(x-1)^2 - 37x

Expand the terms:

36x^2 - 12x + 1 - (30x^2 + 37x + 10) = 6x^2 - 12x - 37x

Combine like terms:

36x^2 - 12x + 1 - 30x^2 - 37x - 10 = 6x^2 - 49x

Move all terms to one side:

36x^2 - 30x^2 - 6x^2 - 12x + 37x + 49x - 1 - 10 = 0

Combine like terms:

0 = 0

This equation is an identity, meaning it is true for all values of x. There are infinitely many solutions.

4. (2x-1)(2x+1) = 2(x-3)^2 = x(2x-3)

Expand the terms:

4x^2 - 1 = 2x^2 - 12x + 18 = 2x^2 - 3x

Combine like terms:

4x^2 - 1 - 2x^2 + 12x - 18 - 2x^2 + 3x = 0

Combine like terms again:

0 = 0

Similar to the previous equation, this is also an identity, and there are infinitely many solutions.

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Next, let's simplify the given expressions and find their values:

1. (a-2b)^2 - (2a-b)^2, if a=-2, b=-3

Substitute the values:

((-2) - 2(-3))^2 - (2(-2) - (-3))^2

Simplify inside the brackets:

(8)^2 - ((-4) + 3)^2

Calculate the squares:

64 - (-1)^2

Finally, calculate the result:

64 - 1 = 63

2. (a^2 - 2)^2 - (a^2 - 1)(a^2 + 2) + 5(a-4)^2, if a = -0.125

Substitute the value:

((-0.125)^2 - 2)^2 - ((-0.125)^2 - 1)((-0.125)^2 + 2) + 5((-0.125)-4)^2

Calculate the values inside the brackets:

((0.015625 - 2))^2 - ((0.015625 - 1)(0.015625 + 2) + 5(-4.125)^2

Simplify further:

(-1.984375)^2 - ((0.984375)(2.015625) + 5(17.578125)

Calculate the squares and products:

3.9375 - (1.984375 + 87.890625)

Add the values:

3.9375 - 89.875

Finally, calculate the result:

-85.9375

3. (m-3)^2 - (m-2)(m+2), if m = -2.5

Substitute the value:

((-2.5)-3)^2 - ((-2.5)-2)((-2.5)+2)

Simplify inside the brackets:

(-5.5)^2 - (-4.5)(-0.5)

Calculate the squares and the product:

30.25 - 2.25

Finally, calculate the result:

28

4. (b^2-1)(b^2+1) - (b^2+2)^2, if b = -3

Substitute the value:

((-3)^2 - 1)((-3)^2 + 1) - ((-3)^2 + 2)^2

Calculate the squares and the product:

(9 - 1)(9 + 1) - (9 + 2)^2

(8)(10) - (11)^2

Calculate the values:

80 - 121

Finally, calculate the result:

-41