Question

СРОЧНО ДОПОМОЖІТЬ БУДЬ ЛАСКА 1. Розв'яжіть рiвняння: a) 4x = 24 + x; б) 4(x - 3) = x + 6; в) 0,3(8 – 3у) = 3,2 – 0,8(у – 7); г)x²-3x=0 д)х²+15х+6=0 e)x4-13x2+36=0 ж) x²-20 X 2x x²-20 =1​

Answer 1

Ответ:

а) 4х=24+х

4х-х=24

3х=24

х=8

б) 4(х-3)=х+6

4х-12=х+6

4х-х=6+12

3х=18

х=6

в) 0,3(8-у)=3,2-0,8(у-7)

2,4-0,9у=3,2-0,8у+5,6

-0,9у+0,8у=3,2+5,6-2,4

-0,1у=6,4

у=-64

г) x²-3x=0

х(х-3)=0

х=0, х-3=0

х=0, х=3

х1=0

х1=3

д) х²+15х+6=0

на фото

e) x•4-13x•2+36=0

4х-26х+36=0

-22х=-36

х=18/11

ж) x²-20 X 2x x²-20 =1

XЄ̶R

Answer 2

a) 4x = 24 + x:

To solve this equation, we want to isolate the variable x on one side of the equation.

Subtract x from both sides: 4x - x = 24 + x - x 3x = 24

Divide both sides by 3: 3x/3 = 24/3 x = 8

Therefore, the solution to the equation 4x = 24 + x is x = 8.

b) 4(x - 3) = x + 6:

Let's simplify the equation first.

Distribute 4 to both terms inside the parentheses: 4x - 12 = x + 6

Next, let's isolate the variable x by moving all the terms involving x to one side of the equation.

Subtract x from both sides: 4x - x - 12 = x - x + 6 3x - 12 = 6

Add 12 to both sides: 3x - 12 + 12 = 6 + 12 3x = 18

Divide both sides by 3: 3x/3 = 18/3 x = 6

Therefore, the solution to the equation 4(x - 3) = x + 6 is x = 6.

c) 0.3(8 - 3y) = 3.2 - 0.8(y - 7):

Let's simplify the equation first.

Distribute 0.3 to both terms inside the parentheses: 0.3 * 8 - 0.3 * 3y = 3.2 - 0.8(y - 7)

Multiply: 2.4 - 0.9y = 3.2 - 0.8y + 5.6

Combine like terms: -0.9y + 0.8y = 3.2 + 5.6 - 2.4

Simplify: -0.1y = 6.4

Divide by -0.1: y = -64

Therefore, the solution to the equation 0.3(8 - 3y) = 3.2 - 0.8(y - 7) is y = -64.

d) x² - 3x = 0:

Factor out x: x(x - 3) = 0

Now we have two factors, and for the equation to equal zero, at least one of the factors must be zero.

So we have two possibilities:

1. x = 0
2. x - 3 = 0

For the second possibility, add 3 to both sides: x - 3 + 3 = 0 + 3 x = 3

Therefore, the solutions to the equation x² - 3x = 0 are x = 0 and x = 3.

e) x⁴ - 13x² + 36 = 0:

Let's solve this equation by introducing a substitution. Let's set y = x².

Substituting y into the equation, we get: y² - 13y + 36 = 0

Now we can solve this quadratic equation for y.

Factorize: (y - 4)(y - 9) = 0

Setting each factor equal to zero, we have: y - 4 = 0 or y - 9 = 0

For the first case, solve for y: y - 4 = 0 y = 4

For the second case, solve for y: y - 9 = 0 y = 9

Now substitute y back in