Step-by-step explanation:
To find the roots (zeroes) of the equation (x+2)^3=x^3-4, we need to set (x+2)^3 equal to zero and solve for x.
First, we can simplify the left side of the equation by expanding (x+2)^3:
(x+2)^3 = (x+2)(x+2)
(x+2) = x^3 + 6x^2 + 12x + 8
Then, we can set this equal to the right side of the equation:
x^3 + 6x^2 + 12x + 8 = x^3 - 4
Subtracting x^3 from both sides gives us:
6x^2 + 12x + 12 = -4
Subtracting 12 from both sides gives us:
6x^2 + 12x = -16
Dividing both sides by 6 gives us:
x^2 + 2x = -2.67
To solve this quadratic equation, we can use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
Plugging in the values for a, b, and c gives us:
x = (-2 +/- sqrt(2^2 - 4 *1 * (-2.67))) / (2 * 1)
This simplifies to:
x = (-2 +/- sqrt(4 + 10.68)) / 2
Which gives us the roots:
x = (-2 + sqrt(14.68)) / 2 = 0.46= -3.46
Therefore, the roots (zeroes) of the equation (x+2)^3=x^3-4 are x = 0.46 and x = -3.46.
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Verified answer
Step-by-step explanation:
To find the roots (zeroes) of the equation (x+2)^3=x^3-4, we need to set (x+2)^3 equal to zero and solve for x.
First, we can simplify the left side of the equation by expanding (x+2)^3:
(x+2)^3 = (x+2)(x+2)
(x+2) = x^3 + 6x^2 + 12x + 8
Then, we can set this equal to the right side of the equation:
x^3 + 6x^2 + 12x + 8 = x^3 - 4
Subtracting x^3 from both sides gives us:
6x^2 + 12x + 12 = -4
Subtracting 12 from both sides gives us:
6x^2 + 12x = -16
Dividing both sides by 6 gives us:
x^2 + 2x = -2.67
To solve this quadratic equation, we can use the quadratic formula:
x = (-b +/- sqrt(b^2 - 4ac)) / (2a)
Plugging in the values for a, b, and c gives us:
x = (-2 +/- sqrt(2^2 - 4 *1 * (-2.67))) / (2 * 1)
This simplifies to:
x = (-2 +/- sqrt(4 + 10.68)) / 2
Which gives us the roots:
x = (-2 + sqrt(14.68)) / 2 = 0.46= -3.46
Therefore, the roots (zeroes) of the equation (x+2)^3=x^3-4 are x = 0.46 and x = -3.46.
what is the radio of the number of girl to the number of boys in the class