It is x = -5
Difference of two cubes: a3 - b3 = (a-b)(a2+ab+b2) 125 - x3 = 53 - x3 = (5 - x)(52 + 5x + x2) = (5 - x)(25 + 5x + x2)
x^(3) + 125 = 0 Remember that 125 = 5^(3) Hence x^(3) + 5^(3) = 0 Factor (x + 5) ( x^(2) - 5x + 25) = 0 So x = -5 & x^(2) - 5x + 125 = 0 Apply Quadratic Eq'n x = {--5 +/- sqrt[)=5)^(2) - 4(1)(125)]} / 2(1) x = { 1 +/- sqrt[25 - 500]} / 2 x = { 1 +/- sqrt[-374] } / 2 This part remain unresolved because you cannot rake the square root of a negative number. Hence x = -5 is the only result.
x3 + 125 Use the sum of two cubes. (x+5)(x2-5x+25)
It is a cubic polynomial in x and its value depends on the value of x.
It is x = -5
Difference of two cubes: a3 - b3 = (a-b)(a2+ab+b2) 125 - x3 = 53 - x3 = (5 - x)(52 + 5x + x2) = (5 - x)(25 + 5x + x2)
x^(3) + 125 = 0 Remember that 125 = 5^(3) Hence x^(3) + 5^(3) = 0 Factor (x + 5) ( x^(2) - 5x + 25) = 0 So x = -5 & x^(2) - 5x + 125 = 0 Apply Quadratic Eq'n x = {--5 +/- sqrt[)=5)^(2) - 4(1)(125)]} / 2(1) x = { 1 +/- sqrt[25 - 500]} / 2 x = { 1 +/- sqrt[-374] } / 2 This part remain unresolved because you cannot rake the square root of a negative number. Hence x = -5 is the only result.
x3 + 125 Use the sum of two cubes. (x+5)(x2-5x+25)
x^(3) + 125 => x^(3) + 5^(3) This factors to (x + 5)(x^(2) - 5x + 5^(2) ) or (x + 5)(x^(2) - 5x + 25) NB The clue is to spot that the constant (125) is a cubic numbers ( 5^(3)). Similarly with other 'cubic factorings'.
It is a cubic polynomial in x and its value depends on the value of x.
X5/X3 5 - 3 = X2 =====That is the exponent part; subtract the bottom exponent from the top exponent. X3/X5 3 - 5 X - 2 =====or, 1/X2 ===
x3 + 5x2 - x - 5 = (x2 - 1)(x + 5) = (x + 1)(x - 1)(x + 5)
5 is a factor of 125 5 x 5 x 5 = 125
I am trying to read this right: (9 x 5) - x3 = ? or 9 x (5 - x3) = ? Which one is it?
5 x 5 x 5 = 125 5 x 25 = 125
x5 / x2 = x3.