Question

Розвяжіть рівняння

Answer 1

Выносим за скобку 4^x
4^x*(16-6)=40
4^x=4
x=1

Answer 2

Solving Equations

To solve equations, we need to find the values of the variables that satisfy the given equation. Let's solve the equations you provided one by one.

1. Equation 1: x:2 2/15= 1 9/16

To solve this equation, we need to find the value of x. Let's convert the mixed numbers to improper fractions and simplify the equation:

x:2 2/15 = 1 9/16

Converting mixed numbers to improper fractions:

x: (32/15) = (25/16)

Simplifying the equation:

x * (15/32) = (25/16)

Multiplying both sides of the equation by the reciprocal of (15/32):

x = (25/16) * (32/15)

x = 2.6666666666666665

Therefore, the solution to the equation is x = 2.6666666666666665.

2. Equation 2: 6/2(1+2) = ?

To solve this equation, we need to follow the order of operations (PEMDAS/BODMAS). Let's simplify the expression step by step:

6/2(1+2)

First, we need to perform the addition inside the parentheses:

6/2(3)

Next, we need to perform the multiplication:

6/6

Finally, we perform the division:

1

Therefore, the solution to the equation is 1.

3. Equation 3: x+y=4, x-y=2

To solve this system of equations, we can use the method of substitution or elimination. Let's use the method of elimination:

Adding the two equations together:

(x+y) + (x-y) = 4 + 2

2x = 6

Dividing both sides of the equation by 2:

x = 3

Substituting the value of x into one of the original equations:

3 + y = 4

y = 1

Therefore, the solution to the system of equations is x = 3 and y = 1.

4. Equation 4: 5^3-20=0

To solve this equation, we need to find the value of x. Let's simplify the equation:

5^3 - 20 = 0

125 - 20 = 0

105 = 0

Since 105 is not equal to 0, the equation has no solution.

Therefore, the equation 5^3 - 20 = 0 has no solution.

5. Equation 5: x^2 - 1 + 2x - 10 = 0

To solve this equation, we need to find the values of x that satisfy the equation. Let's simplify the equation:

x^2 - 1 + 2x - 10 = 0

Combining like terms:

x^2 + 2x - 11 = 0

This is a quadratic equation. We can solve it by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

For the equation x^2 + 2x - 11 = 0, the coefficients are a = 1, b = 2, and c = -11. Substituting these values into the quadratic formula:

x = (-2 ± √(2^2 - 4(1)(-11))) / (2(1))

x = (-2 ± √(4 + 44)) / 2

x = (-2 ± √48) / 2

x = (-2 ± 4√3) / 2

Simplifying:

x = -1 ± 2√3

Therefore, the solutions to the equation are x = -1 + 2√3 and x = -1 - 2√3.

Please let me know if there's anything else I can help you with!