To find the value of x^3-8, we need to first find the value of x that satisfies the equation x+4/x=2. We can do this by cross-multiplying and rearranging the terms:
x^2 + 4 = 2x x^2 - 2x + 4 = 0
This is a quadratic equation, which can be solved by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = -2, and c = 4. Plugging these values into the formula, we get:
x = (2 ± √((-2)^2 - 4(1)(4))) / 2(1) x = (2 ± √(-12)) / 2 x = (2 ± 2√(-3)) / 2 x = 1 ± √(-3)
Since x is a complex number, we can write it in the form of a + bi, where a and b are real numbers and i is the imaginary unit:
x = 1 ± √(-3)i
Now, we can use the binomial theorem to find the value of x^3:
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Step-by-step explanation:
To find the value of x^3-8, we need to first find the value of x that satisfies the equation x+4/x=2. We can do this by cross-multiplying and rearranging the terms:
x^2 + 4 = 2x x^2 - 2x + 4 = 0
This is a quadratic equation, which can be solved by using the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a
where a = 1, b = -2, and c = 4. Plugging these values into the formula, we get:
x = (2 ± √((-2)^2 - 4(1)(4))) / 2(1) x = (2 ± √(-12)) / 2 x = (2 ± 2√(-3)) / 2 x = 1 ± √(-3)
Since x is a complex number, we can write it in the form of a + bi, where a and b are real numbers and i is the imaginary unit:
x = 1 ± √(-3)i
Now, we can use the binomial theorem to find the value of x^3:
x^3 = (1 ± √(-3)i)^3 x^3 = (1 ± √(-3)i)(1 ± √(-3)i)(1 ± √(-3)i) x^3 = (1 ± 2√(-3)i - 3)(1 ± √(-3)i) x^3 = (1 - 2√(-3)i - 3) ± (2√(-3)i - 3√(-3)i + 3i) x^3 = (-2 - 2√(-3)i) ± (-√(-3)i + 3i) x^3 = -2 ± 2i ± (-√(-3) + 3)i
Finally, we can subtract 8 from both values of x^3 to get the answer:
x^3 - 8 = (-2 ± 2i ± (-√(-3) + 3)i) - 8 x^3 - 8 = -10 ± 2i ± (-√(-3) + 3)i
This is the value of x^3 - 8 when x + 4/x = 2. You can also use a solve for x calculator to check your answer. I hope this helps you.
this is the answer
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