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 ===
We note that '125' ends in '5'. So it will divide by '5', which is a prime number. Hence 5)125 5)25 5)5 = 1 Keep dividing by any prime number, that will go into the answer, in this case '5'. So 5 x 5 x 5 = 5^(3) = 125 NB Any number that ends in '5' or '0' will divide by '5'. Any number that ends with an EVEN number will divide by '2'. Any number were the digits sum to '9' will divide by '9'. e.g. 27 ; 2 + 7 = 9 27/9 = 3
x3 + 5x2 - x - 5 = (x2 - 1)(x + 5) = (x + 1)(x - 1)(x + 5)
I am trying to read this right: (9 x 5) - x3 = ? or 9 x (5 - x3) = ? Which one is it?
5 is a factor of 125 5 x 5 x 5 = 125
5 x 5 x 5 = 125 5 x 25 = 125