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zysi [14]
3 years ago
6

Given that the quadratic equation has equal roots (k^2-1)x^2-2kx-3k-1=0

Mathematics
1 answer:
Alik [6]3 years ago
7 0

Answer:

(See explanation for further details)

Step-by-step explanation:

The real expression is:

(k^{2}-1)\cdot x{{2} - 2\cdot k \cdot x - 3\cdot k + 1 = 0

The general equation for the second-order polynomial is:

x = \frac{2\cdot k \pm \sqrt{4\cdot k^{2}-4\cdot (k^{2}-1)\cdot (-3\cdot k + 1)}}{k^{2}-1}

This condition must be observed for the case of a quadratic equation with equal roots:

4\cdot k^{2} - 4\cdot (k^{2}-1)\cdot (-3\cdot k + 1) = 0

k^{2} + (k^{2}-1)\cdot (3\cdot k + 1) = 0

k^{2} + 3\cdot k^{3} - 3\cdot k - k^{2}-1 = 0

3\cdot k^{3} - 3\cdot k - 1 = 0

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Answer:

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Step-by-step explanation:

Given: i. for the cylinder, base radius = 2x cm, height = h cm

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volume of a cylinder is given as;

volume = \frac{1}{3}\pir^{2}h

where: r is its base radius and h the height

volume of the given cylinder = \frac{1}{3}\pi x (2x)^{2} x h

                                              = \frac{1}{3}\pi x 4x^{2} x h

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volume of a sphere = \frac{4}{3}\pir^{3}

where r is the radius.

volume of the given sphere =  \frac{4}{3}\pi x (3x)^{3}

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Since,

volume of the cylinder = volume of the sphere

Then we have;

\frac{4}{3}\pix^{2} h = 12\pix^{3}

4\pix^{2} h = 36\pix^{3}

subtract x^{2} from both sides

4\pih = 36\pix

divide both sides by 4\pi

h = \frac{36\pi x}{4\pi }

  = 9x

h = 9x

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