Question

(3x-1)(3x+1)=(2x+1)²+x-2​

Answer 1

Ответ:

(3x-1)(3x+1)=(2x+1)²+x-2​

(a-b)(a+b)=a²-b²; (a+b)²=a²+2ab+b²

9x²-1=4х²+4х+1+х-2

9х²-1=4х²+5х-1

9х²=4х²+5х

9х²-4х²-5х=0

х(9х-4х-5)=0

х(5х-5)=0

х⋅5(х-1)=0

х(х-1)=0

х=0

х-1=0

х1=0,х2=1

Answer 2

Let's solve the given equation step by step.

Starting with the left side of the equation:

(3x - 1)(3x + 1)

Using the formula (a + b)(a - b) = a^2 - b^2, we can simplify this expression:

(3x)^2 - (1)^2 9x^2 - 1

Now, let's simplify the right side of the equation:

(2x + 1)^2 + x - 2

Expanding the square:

(2x + 1)(2x + 1) (2x)^2 + 2(2x)(1) + (1)^2 4x^2 + 4x + 1 + x - 2 4x^2 + 5x - 1

Now, we can rewrite the equation using the simplified expressions:

9x^2 - 1 = 4x^2 + 5x - 1

Let's simplify it further:

9x^2 - 4x^2 - 5x = 0

Combining like terms:

5x^2 - 5x = 0

Factoring out the common factor of 5x:

5x(x - 1) = 0

Now, we can set each factor equal to zero and solve for x:

5x = 0 x = 0

x - 1 = 0 x = 1

Therefore, the solutions to the equation are x = 0 and x = 1.