Question

(х-5)²=16 решить уравнение

Answer 1

x^2-10x+25=16

x^2-10x+9=0

x1+x2=10

x1*x2=9

x1=9

x2=1

Answer 2

x^2-10x+25=16

x^2-10x+9=0

D=100-36=64

x1,2=(10+-√64):2

x1=9

x2=1

Answer 3

To solve the equation (х-5)²=16, you can follow these steps:

Step 1: Expand the square on the left side of the equation. Step 2: Set the equation equal to zero. Step 3: Factor the resulting quadratic equation. Step 4: Solve for the variable х.

Let's go through each step:

Step 1: Expand the square (х-5)². (х-5)² = (х-5)(х-5) = х² - 2х*5 + 5² = х² - 10х + 25

Step 2: Set the equation equal to zero. х² - 10х + 25 = 16

Step 3: Rewrite the equation in standard quadratic form (ax² + bx + c = 0). х² - 10х + 25 - 16 = 0 х² - 10х + 9 = 0

Step 4: Factor the quadratic equation or use the quadratic formula to find the solutions for х. Let's factor this equation:

(х - 9)(х - 1) = 0

Now, use the zero product property which states that if the product of two factors is equal to zero, then at least one of the factors must be zero:

1. х - 9 = 0 х = 9

2. х - 1 = 0 х = 1

So, the solutions to the equation (х-5)²=16 are х = 9 and х = 1.