Question

(х+2)^2=(x+4)^2 в ответе укажите больший корень ответ :-3

Answer 1

Ответ:

-3

Пошаговое объяснение:

$(x+2)^2=(x+4)^2\\ \\ (x+2)^2-(x+4)^2=0\\ \\ (x+2+x+4)(x+2-x-4)=0\\ \\ (2x+6)*(-2)=0\\ \\ 2x+6=0\\ \\ x=-3$

Answer 2

To solve the given equation, expand both sides and then solve for the value of "x":

Expand the left side: (х + 2)^2 = (x + 2)(x + 2) = x^2 + 4x + 4

Expand the right side: (x + 4)^2 = (x + 4)(x + 4) = x^2 + 8x + 16

Now set the two expressions equal to each other: x^2 + 4x + 4 = x^2 + 8x + 16

Next, move all terms to one side of the equation: x^2 + 4x + 4 - x^2 - 8x - 16 = 0

Simplify the equation: -4x - 12 = 0

Now, solve for "x": -4x = 12 x = -12 / -4 x = 3

The two possible solutions for "x" are x = 3 and x = -3.

However, we need to check which one gives the larger root when substituted back into the original equation:

For x = 3: (3 + 2)^2 = (3 + 4)^2 5^2 = 7^2 25 ≠ 49

For x = -3: (-3 + 2)^2 = (-3 + 4)^2 (-1)^2 = 1^2 1 = 1

So, the larger root is x = -3, and the answer is -3.