Question

Запишите в ответе номера верных равенств1) (c-4)(4+c)=16-c^22) -(6-5c)(5c+6)=36-25c^23) (c+3)(3-4c)=9-9c-4c^24) (6-c)^2=36-6c+c^2

Answer 1

(c-4)(4+c)=16-c^2
c^2-16≠16-c^2

-(6-5c)(5c+6)=36-25c^2
-(36-25c^2)=36-25c^2
25c^2-36≠36-25c^2

(c+3)(3-4c)=9-9c-4c^2
3c-4c^+9-12c=9-9c-4c^2
9-9c-4c^2=9-9c-4c^2

(6-c)^2=36-6c+c^2
36-12c+c^2$\neq$36-6c+c^2

следовательно верные:3

Answer 2

3,4 - верные
у меня так получилось

Answer 3

1) (c-4)(4+c) = 16 - c^2 Expanding the expression using the distributive property: (c-4)(4+c) = 4(c-4) + c(c-4) = 4c - 16 + c^2 - 4c = c^2 - 16

So, the equation simplifies to: c^2 - 16 = 16 - c^2

Adding c^2 to both sides of the equation: 2c^2 - 16 = 16

Adding 16 to both sides of the equation: 2c^2 = 32

Dividing both sides of the equation by 2: c^2 = 16

Taking the square root of both sides of the equation: c = ±4

Therefore, the solutions to the equation are c = 4 and c = -4.

2) (6-5c)(5c+6) = 36 - 25c^2 Expanding the expression using the distributive property: (6-5c)(5c+6) = 6(5c+6) - 5c(5c+6) = 30c + 36 - 25c^2 - 30c = 36 - 25c^2

So, the equation simplifies to: 36 - 25c^2 = 36 - 25c^2

This equation is an identity, which means that it holds true for all values of c. Therefore, there are infinite solutions to this equation.

3) (c+3)(3-4c) = 9 - 9c - 4c^2 Expanding the expression using the distributive property: (c+3)(3-4c) = 3(c+3) - 4c(c+3) = 3c + 9 - 4c^2 - 12c = -4c^2 - 9c + 9

So, the equation simplifies to: -4c^2 - 9c + 9 = 9 - 9c - 4c^2

Adding 4c^2 to both sides of the equation: -9c + 9 = 9 - 9c

Subtracting 9 from both sides of the equation: -9c = 0

Dividing both sides of the equation by -9: c = 0

Therefore, the solution to the equation is c = 0.

4) (6-c)^2 = 36 - 6c + c^2 Expanding the expression using the distributive property: (6-c)^2 = (6-c)(6-c) = 6(6-c) - c(6-c) = 36 - 6c - 6c + c^2 = 36 - 12c + c^2

So, the equation simplifies to: 36 - 12c + c^2 = 36 - 6c + c^2

Subtracting 36 from both sides of the equation: -12c = -6c

Dividing both sides of the equation by -6: c = 0

Therefore, the solution to the equation is c = 0.

In summary, the solutions to the given equations are: 1) c = 4, c = -4 2) Infinite solutions 3) c = 0 4) c = 0