Question

(3х+1)(3х-1)-(х+2)(х-1)=8

Answer 1

(3х+1)(3х-1)-(х+2)(х-1)=8

9x²-1-(x²-x+2x-2)=8

9x²-1-x²+x-2x+2-8=0

8x²-x-7=0

D=1+4*7*8=225

x=(1-15)/16=-14/16=-7/8

x=(1+15)/16=1

ответ: -7/8, 1

Answer 2

Let's solve the given equation step by step:

Step 1: Expand the expressions on both sides of the equation. Using the distributive property, we get:

(3x + 1)(3x - 1) - (x + 2)(x - 1) = 8 (9x^2 - 3x - 3x + 1) - (x^2 - x - 2x + 2) = 8 (9x^2 - 6x + 1) - (x^2 - 3x + 2) = 8

Step 2: Combine like terms. Now, let's combine the like terms:

9x^2 - 6x + 1 - x^2 + 3x - 2 = 8

Step 3: Simplify the equation. Combine the remaining like terms:

8x^2 - 3x - 1 = 8

Step 4: Move all terms to one side to set the equation to zero. Subtract 8 from both sides to set the equation to zero:

8x^2 - 3x - 9 = 0

Step 5: Solve the quadratic equation. Now, we need to solve the quadratic equation. We can use the quadratic formula:

The quadratic formula is given by: x = (-b ± √(b^2 - 4ac)) / 2a

In our case, a = 8, b = -3, and c = -9. Let's plug these values into the formula:

x = (3 ± √((-3)^2 - 4 * 8 * -9)) / 2 * 8 x = (3 ± √(9 + 288)) / 16 x = (3 ± √297) / 16

Step 6: Simplify the solutions. We can simplify the solutions further:

x = (3 + √297) / 16 or x = (3 - √297) / 16

These are the two solutions to the equation. Keep in mind that √297 is an irrational number, so the exact values would be in terms of the square root. If you need approximate numerical values, you can use a calculator to find them.