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Ivenika [448]
3 years ago
14

Determine the followingquadratic equations have realroots1) 3x² - √2x-√3​

Mathematics
1 answer:
IceJOKER [234]3 years ago
3 0

Step-by-step explanation:

√3 x² - 2x - √3 = 0

√3 x² - 3x + x - √3 = 0

√3 x(x - √3) + 1(x - √3) = 0

(x - √3 ) (√3 x + 1) = 0

x - √3 = 0 , √3 x +1 = 0

x = √3 , x = -1/√3

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Answer:

<h2>            A = 27(2√3-π) cm² ≈ 8.71 cm²</h2>

Step-by-step explanation:

Area of shaded region it is area of hexagon minus area of circle.

A regular hexagon is comprised of six equilateral triangles (of the same sides).

So its area:  A_1=6\cdot\dfrac{S^2\sqrt3}{4}=\dfrac{3S^2\sqrt3}2     {S = side of the triangle}

Height (H) of such a triangle is equal to radius (R) of a circle inscribed in the hexagon:

R = H = \dfrac{S\sqrt3}{2}

Area of shaded region:

A=A_1-A_\circ=\dfrac{3S^2\sqrt3}2-\pi R^2=\dfrac{6S^2\sqrt3}4-\pi\left(\dfrac{S\sqrt3}2\right)^2=\dfrac{S^2(6\sqrt3-3\pi)}4

S = 6 cm

so:

A=\dfrac{6^2(6\sqrt3-3\pi)}4=\dfrac{36(6\sqrt3-3\pi)}4=9(6\sqrt3-3\pi)=27(2\sqrt3-\pi)\ cm^2\\\\A=27(2\sqrt3-\pi)\ cm^2\approx8.71\ cm^2

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