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We have the function as

f(X)=x^4-x^3

We have x^4-x^3=75

x^4-x^3-75=0

Let g(X)=x^4-x^3-75

g(3)=81-27-75=-21

g(4)=4^4-4^3-75=117

As the g(3) value is negative and the g(4) value is positive it implies that the function has a solution in the interval in the [3,4] as the graph crosses the x-axis in this interval.