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Why does a cube root only have one value?
Because the cube of a positive number is positive and the cube of a negative number is negative.-------------------------------------------------------------------------------------------------------------------------------Every number has THREE cube roots. However, (at least) two of the three are complex numbers.For example, the cube roots of 8 are 2, (-1 + √3 i) and (-1 - √3 i) with i² = -1:2³ = 2 × 2 × 2 = 8(-1 + √3 i)³ = (-1 + √3 i)(-1 + √3 i)(-1 + √3 i)= (-1 + √3 i)((-1)² - 2√3 i + 3i²)= (-1 + √3 i)(1 - 2√3 i -3)= (-1 + √3 i)(-2 - 2√3 i)= (-1 + √3 i)(-1 - √3 i)2= ((-1)² - 3i²)2= (1 + 3)2= 4 × 2 = 8(-1 - √3 i)³ = (-1 - √3 i)(-1 - √3 i)(-1 - √3 i)= (-1 - √3 i)((-1)² + 2√3 i + 3i²)= (-1 - √3 i)(1 + 2√3 i -3)= (-1 - √3 i)(-2 + 2√3 i)= (-1 - √3 i)(-1 + √3 i)2= ((-1)² - 3i²)2= (1 + 3)2= 4 × 2 = 8
How many different equations can be made with the numbers 0123?
A huge number. 0 + 1 + 2 = 3 0 + 2 + 1 = 3 1 + 0 + 2 = 3 1 + 2 + 0 = 3 2 + 0 + 1 = 3 2 + 1 + 0 = 3 -0 + 1 + 2 = 3 -0 + 2 + 1 = 3 1 - 0 + 2 = 31 + 2 - 0 = 32 - 0 + 1 = 32 + 1 - 0 = 3 0 - 1 + 3 = 2 0 + 3 - 1 = 2 -1 + 0 + 3 = 2 -1 + 3 + 0 = 2 3 + 0 - 1 = 2 3 - 1 + 0 = 2 -0 - 1 + 3 = 2-0 + 3 - 1 = 2-1 - 0 + 3 = 2-1 + 3 - 0 = 23 - 0 - 1 = 23 - 1 - 0 = 2 0 - 2 + 3 = 1 0 + 3 - 2 = 1 -2 + 0 + 3 = 1 -2 + 3 + 0 = 1 3 + 0 - 2 = 1 3 - 2 + 0 = 1 -0 - 2 + 3 = 1-0 + 3 - 2 = 1-2 - 0 + 3 = 1-2 + 3 - 0 = 13 - 0 - 2 = 13 - 2 - 0 = 1 1 + 2 - 3 = 0 1 - 3 + 2 = 0 2 + 1 - 3 = 0 2 - 3 + 1 = 0 -3 + 1 + 2 = 0 -3 + 2 + 1 = 0 For each of these equations there is a counterpart in which all signs have been switched. For example 0 + 1 + 2 = 3 gives -0 - 1 - 2 = -3and so on. Now, all of the above equations has three numbers on the left and one on the right. Each can be converted to others with two numbers on each side. For example:the equation 0 + 1 + 2 = 3 gives rise to0 + 1 = 3 - 20 + 1 = -2 + 30 + 2 = 3 - 10 + 2 = -1 + 31 + 2 = 3 - 01 + 2 = -0 + 3-0 + 1 = 3 - 2-0 + 1 = -2 + 3-0 + 2 = 3 - 1-0 + 2 = -1 + 31 + 2 = 3 + 01 + 2 = +0 + 3 As you can see, the number of equations is huge!
What is 1 half add 1 and a half times by 2?
1/2 + (11/2)*2 = 1/2 + (3/2)*2 = 1/2 + 3 = 31/21/2 + (11/2)*2 = 1/2 + (3/2)*2 = 1/2 + 3 = 31/21/2 + (11/2)*2 = 1/2 + (3/2)*2 = 1/2 + 3 = 31/21/2 + (11/2)*2 = 1/2 + (3/2)*2 = 1/2 + 3 = 31/2
Adding two cube's equal to 9 i want two answers?
1^3 + 2^3 = 1 + 8 = 9 2^3 + 1^3 = 8 + 1 = 9 There is also: 1^3 + (-1 + i√3)^3 = 9 1^3 + (-1 - i√3)^3 = 9 (-1/2 + i√3/2)^3 + 2^3 = 9 (-1/2 - i√3/2)^3 + 2^3 = 9
How do you get the answer 7 using only numbers -4-3-2-1?
[(-4) + (-3)]*[(-2 - (-1)] = (-4 -3)*(-2 + 1) = -7*-1 = +7[(-4) + (-3)]*[(-2 - (-1)] = (-4 -3)*(-2 + 1) = -7*-1 = +7[(-4) + (-3)]*[(-2 - (-1)] = (-4 -3)*(-2 + 1) = -7*-1 = +7[(-4) + (-3)]*[(-2 - (-1)] = (-4 -3)*(-2 + 1) = -7*-1 = +7
