Question

(3х - 1)(3х + 1) – (х - 1)(х + 2) = 8

Answer 1

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

8x^2+1-x-8=0

8x^2-x-7=0

D=(-1)^2+4×7×8=225

x=1

x=-15/16

Answer 2

Объяснение:

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

8x^2 +1 -x=8

8x^2 - x= 7

8x^2 - x - 7 =0

D= 1 + 4×8×7=225=15^2

x1= 1 - 15 / 16 = - 14/16 = -7/8

x2= 1 +15/16 = 1

1 и -7/8

Answer 3

Let's solve the given equation step by step:

(3x - 1)(3x + 1) - (x - 1)(x + 2) = 8

Expanding the expressions within the parentheses:

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

Removing the parentheses:

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

Combining like terms:

8x^2 - x + 1 = 8

Moving all terms to one side:

8x^2 - x + 1 - 8 = 0

8x^2 - x - 7 = 0

Now, we have a quadratic equation in standard form (ax^2 + bx + c = 0) with a = 8, b = -1, and c = -7.

To solve this quadratic equation, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

Substituting the values:

x = (-(-1) ± √((-1)^2 - 4(8)(-7))) / (2(8))

Simplifying further:

x = (1 ± √(1 + 224)) / 16

x = (1 ± √225) / 16

x = (1 ± 15) / 16

Now we have two possible solutions:

x1 = (1 + 15) / 16 = 16 / 16 = 1

x2 = (1 - 15) / 16 = -14 / 16 = -7/8

Therefore, the solutions to the equation (3x - 1)(3x + 1) - (x - 1)(x + 2) = 8 are x = 1 and x = -7/8.