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telo118 [61]
2 years ago
7

Solve each equation, if possible. Write irrational numbers in simplest radical form. Describe the strategy you used to get your

solution and tell why you chose that strategy.
〖3x〗^2+27=0
x^2-8x+1=0
Mathematics
1 answer:
VladimirAG [237]2 years ago
8 0
Problem 1
Do you know what a complex number is? If you do not, you can get an answer but not one you will like much.

(3x)^2 + 27 = 0               remove the brackets. Remember to square what's inside the brackets.

9x^2 + 27 = 0                Divide both terms by 9
9x^2/9 + 27/9 = 0

x^2 + 3 =  0                  Subtract 3 from both sides.
x^2 = -3                        Take the square root from both sides.
x = sqrt(-3)                    but the square root of - 3 = 3i
x = i*sqrt(3)

Problem 2
x^ - 8x + 1 = 0
a = 1
b = - 8
c = 1

x = [- -8 +/- sqrt(b^2 - 4*a*c) ]/(2*a)     Quadratic formula
x = [ 8 +/- sqrt( (-8)^2 - 4(1*1)]/2          Substitute Givens and combine
x = [ 8 +/- sqrt( 64 - 4 )] /2                    Subtract 4
x = [ 8 +/- sqrt (60)]/2                            Break 60 into 4 * 15 
x = [ 8 +/- sqrt (4*15)]/2                         Notice 4 is a perfect square. sqrt4 = 2
x = [ 8 +/- 2*sqrt(15)] / 2                        Divide through by 2
x = 8/2 +/- sqrt (15)
x = 4 +/- sqrt(15) the twos were gone
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                            =       12 x 6

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          Volume = Base Depth

                            =  Width x Depth x Heigh

                            =    2 x 2 x 1  

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      How many smaller cubes can be made?

            The obvious answer might be to straight up divide the large cube volume by the smaler cuboid volume. That might work IF all of the cuboid dimensions divide evenly into the cube dimensions.

  Number of cuboid  =   Volume of the cube  /  Volume of the cuboid

                                  =             72 / 4

                                  =        18

Check this answer by dividing the dimension of the cube by the cuboid

         4 by 6 by 3

         2 by 2 by 1

      (4/2) by (6/2) by (3/1)

        2    by    3   by     3       = 2 x 3 x 3     =    18

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