Question

1) (1,6*10^-5)(4*10^2) 2)18-х^2=14 3) х^2+2=х+2 4) х(х+3)=4 5)х(х-4)=-3

Answer 1

1) (1,6*10⁻⁵)(4*10²) = 6,4*10²⁻⁵ = 6,4*10⁻³
2) 18 - х² = 14
     18 - 14 = х²
         х² = 4
         х = 2;  х = -2

3) x² + 2 = x + 2
     x² - x = 0
     x(x - 1) = 0
     x = 0;   x = 1

4) x(x + 3) = 4
     x² + 3x - 4 = 0     D = b²-4ac = 9+16 = 25
     x₁ = (-b+√D)/2a = (-3+5)/2 = 1
     x₂ = (-b-√D)/2a = (-3-5)/2 = -4

5) x(x - 4) = -3
     x² - 4x + 3 = 0     D = b²-4ac = 16-12 = 4
     x₁ = (-b+√D)/2a = (4+2)/2 = 3
     x₂ = (-b-√D)/2a = (4-2)/2 = 1  

Answer 2

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

1. (1.6 * 10^-5) * (4 * 10^2): First, multiply the numbers outside of the parentheses: (1.6 * 4) * (10^-5 * 10^2) 6.4 * (10^-5 * 10^2)

   Now, let's simplify the powers of 10: 6.4 * 10^(-5 + 2)

   Add the exponents: 6.4 * 10^(-3)

   So, (1.6 * 10^-5) * (4 * 10^2) = 6.4 * 10^(-3).

2. 18 - x^2 = 14: First, subtract 14 from both sides of the equation to isolate x^2: 18 - 14 - x^2 = 14 - 14 4 - x^2 = 0

   Now, add x^2 to both sides to isolate the x^2 term: 4 - x^2 + x^2 = 0 + x^2 4 = x^2

   To solve for x, take the square root of both sides: √4 = √(x^2) 2 = x

   So, the solution is x = 2.

3. x^2 + 2 = x + 2: Subtract 2 from both sides of the equation to isolate the x^2 term: x^2 + 2 - 2 = x + 2 - 2 x^2 = x

   So, the solution is x^2 = x.

4. x(x + 3) = 4: Distribute x on the left side of the equation: x^2 + 3x = 4

   Subtract 4 from both sides to set the equation equal to zero: x^2 + 3x - 4 = 0

   Now, you can factor or use the quadratic formula to solve for x. Factoring: (x + 4)(x - 1) = 0

   Setting each factor equal to zero: x + 4 = 0 or x - 1 = 0

   Solving for x in each equation: x = -4 or x = 1

   So, the solutions are x = -4 and x = 1.

5. x(x - 4) = -3: Distribute x on the left side of the equation: x^2 - 4x = -3

   Add 3 to both sides to set the equation equal to zero: x^2 - 4x + 3 = 0

   Now, you can factor or use the quadratic formula to solve for x. Factoring: (x - 3)(x - 1) = 0

   Setting each factor equal to zero: x - 3 = 0 or x - 1 = 0

   Solving for x in each equation: x = 3 or x = 1

   So, the solutions are x = 3 and x = 1.