Is there a number that is exactly 1 more than

rabbitz42z8

rabbitz42z8

Answered question

2021-11-12

Is there a number that is exactly 1 more than its cube?

Answer & Explanation

George Woody

George Woody

Beginner2021-11-13Added 16 answers

Where x is a number equal to 1 more than its cube
x=x3+1
f(x) is the equation for a number whose cube is one less than the numerator
x3x+1=0=f(x)
Try plugging in different values for x to get an outputs above and below f(x)=0. We used f(2) and f(2) to get -5 and 7
(2)3(2)+1=5
but
(2)3(2)+1=7
The intermediate value theorem states that if a function is continuous between (a,b), it takes on every value between f(a) and f(b). We know that x3x+1 is continuous because it is a polynomial
f(x) is continuous between (-2,2), so it will take on every value between f(2) to f(2), or between [-5,7]. Because 0 is included in this interval, then the value f(x)=0 exists.

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