Question

X-5x+6=0 x-8x+7=0 x-9x+8=0

Answer 1

1) - 4х = - 6
х = 6/4 = 3/2 = 1 1/2
2) - 7х = - 7
х = 1
3) - 8х = - 8
х = 1

Answer 2

$1) x^2-5x+6=0 D=25-24=1 x_1=(5+1)/2 = 3; x_2 = (5-1) / 2=2$

$2)x^2-8x+7=0 D=(-8)^2-4*1*7=64-28=36 \sqrt{D}=6 x_1=(-(-8)+6)/2*1=(8+6)/2=7 x_2=(8-6)/2*1=(2)/2=1$

$3)x^2-9x+8=0 D= 81-4*7=49; \sqrt{D} = 7 x_1=(9+7)/2=8 x_2=(9-7)/2=1$

Ответ: 
1) x_1= 3; x_2= 2;
2) x_1= 7; x_2= 1;
3) x_1= 8; x_2= 1.

Answer 3

To solve each of these equations, we can use the quadratic formula. The quadratic formula is given by:

x = (-b ± √(b^2 - 4ac)) / (2a)

Let's solve each equation step by step:

1. x - 5x + 6 = 0 Rearranging the terms, we get: -4x + 6 = 0 Comparing this equation to the general form ax^2 + bx + c = 0, we have a = -4, b = 0, and c = 6. Substituting these values into the quadratic formula: x = (-0 ± √(0^2 - 4(-4)(6))) / (2(-4)) x = (± √(0 - (-96))) / (-8) x = (± √96) / (-8) Simplifying further, we have: x = ± √(96) / (-8) x = ± √(16 * 6) / (-8) x = ± (4√6) / (-8) Simplifying the fraction, we get: x = ± (√6) / (-2) So the solutions are: x = -√6 / 2 and x = √6 / -2, or simply x = -√6 / 2 and x = √6 / 2.

2. x - 8x + 7 = 0 Rearranging the terms, we get: -7x + 7 = 0 Comparing this equation to the general form ax^2 + bx + c = 0, we have a = -7, b = 0, and c = 7. Substituting these values into the quadratic formula: x = (-0 ± √(0^2 - 4(-7)(7))) / (2(-7)) x = (± √(0 - (-196))) / (-14) x = (± √(196)) / (-14) Simplifying further, we have: x = ± (14) / (-14) x = ± 1 So the solutions are: x = -1 and x = 1.

3. x - 9x + 8 = 0 Rearranging the terms, we get: -8x + 8 = 0 Comparing this equation to the general form ax^2 + bx + c = 0, we have a = -8, b = 0, and c = 8. Substituting these values into the quadratic formula: x = (-0 ± √(0^2 - 4(-8)(8))) / (2(-8)) x = (± √(0 - (-256))) / (-16) x = (± √(256)) / (-16) Simplifying further, we have: x = ± (16) / (-16) x = ± 1 So the solutions are: x = -1 and x = 1.

Therefore, the solutions to the given equations are as follows:

Equation 1: x = -√6 / 2 and x = √6 / 2 Equation 2: x = -1 and x = 1 Equation 3: x = -1 and x = 1