Question

(11x+2)(11x-2)-(11x-1)^2=61​

Answer 1

a² - b² = (a - b)(a + b)

(a - b)² = a² - 2ab + b²

(11x+2)(11x-2)-(11x-1)²=61​

(11x)² - 2² - ((11x)² - 2*1*11x + 1²) = 61

121x² - 4 - 121x² + 22x - 1 = 61

22x = 66

x = 66 : 22

x = 3

Answer 2

Ответ:

$x=3.$

Пошаговое объяснение:

$(11x+2)(11x-2)-(11x-1)^2=61\\(11x)^2-2^2-((11x)^2-2\cdot11x\cdot1+1^2)=61\\121x^2-4-(121x^2-22x+1)=61\\121x^2-4-121x^2+22x-1=61\\22x=61+4+1\\22x=66\\x=66:22\\x=3.$

Проверка:

$(11\cdot3+2)(11\cdot3-2)-(11\cdot3-1)^2=61\\(33+2)(33-2)-(33-1)^2=61\\35\cdot31-32^2=61\\1085-1024=61\\61=61.$

Answer 3

To solve the equation (11x+2)(11x-2) - (11x-1)^2 = 61, you can follow these steps:

1. Expand the expressions: (11x+2)(11x-2) = 121x^2 - 4 (11x-1)^2 = 121x^2 - 22x + 1

2. Rewrite the equation with the expanded expressions: 121x^2 - 4 - (121x^2 - 22x + 1) = 61

3. Simplify the equation: 121x^2 - 4 - 121x^2 + 22x - 1 = 61

4. Combine like terms: (121x^2 - 121x^2) + (22x - 4 - 1) = 61

5. Further simplify: 22x - 5 = 61

6. Isolate the variable x: 22x = 61 + 5 22x = 66

7. Divide by 22 to solve for x: x = 66 / 22 x = 3

So, the solution to the equation is x = 3.