Question

let 2 X bi x square - 16 - three bi x minus 4 is equals to 5 by X + 4 if x is equals to k by 3 e then k is equals to

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Answer 1

Step-by-step explanation:

We are given the equation:

2bi(x^2) - 16 - 3bi(x) - 4 = 5/(x+4)

We are also told that x = k/3e. Substituting this value into the equation, we get:

2bi(k^2)/(9e^2) - 16 - 3bi(k)/(3e) - 4 = 5/(k/3e + 4)

Simplifying the right-hand side, we get:

5/(k/3e + 4) = 15e/(k+12e)

Substituting this back into the equation and multiplying both sides by k+12e to eliminate the fraction, we get:

2bi(k^2)/(9e^2) - 16 - 3bi(k)/(3e) - 4 = 15e/(k+12e)

Multiplying both sides by 9e^2 to eliminate the denominators, we get:

2bi(k^2) - 144e^2 - 27bi(k)e - 36e^3 = 135e(k^2 + 24ke + 144e^2)

Simplifying and rearranging, we get:

2bi(k^2) - 135ek^2 - 27bi(k)e - 360e^3 = 0

Dividing both sides by k (which we can do because k ≠ 0), we get:

2bi(k) - 135e - 27bi(e)/k - 360e^3/k = 0

Multiplying both sides by k to eliminate the fraction, we get:

2bi(k^2) - 135ek - 27bi(e) - 360e^3 = 0

This is a quadratic equation in k, which we can solve using the quadratic formula:

k = [135e ± sqrt((135e)^2 - 4(2bi)(-27bi(e)-360e^3))] / (4bi)

Simplifying under the square root, we get:

k = [135e ± sqrt(18225e^2 + 2160bi(e^4))] / (4bi)

Therefore, k is equal to:

k = [135e + sqrt(18225e^2 + 2160bi(e^4))] / (4bi)

or

k = [135e - sqrt(18225e^2 + 2160bi(e^4))] / (4bi)