SOLUTION: one dimension of a cube is increased by 1 inch to form a rectangular bloc.Suppose that the volume of the new block is 150 cubic inches.Find the length of an edge of the original cu

Algebra ->  Rectangles -> SOLUTION: one dimension of a cube is increased by 1 inch to form a rectangular bloc.Suppose that the volume of the new block is 150 cubic inches.Find the length of an edge of the original cu      Log On


   

Question 1143777: one dimension of a cube is increased by 1 inch to form a rectangular bloc.Suppose that the volume of the new block is 150 cubic inches.Find the length of an edge of the original cube
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39626) About Me  (Show Source):
You can put this solution on YOUR website!
x, dimension of original cube, each of the three directions

x%2Ax%2A%28x%2B1%29=150

x%5E3%2Bx%5E2=150

x%5E3%2Bx%5E2-150=0

Check if 3 or 5 is a root for the cubic equation.
(In fact, one root is x=5 ).

check:
5%2A5%2A%285%2B1%29
25%2A6
150
checks.

Answer by ikleyn(52863) About Me  (Show Source):
You can put this solution on YOUR website!
.

(x+1)*x*x = 150.


One solution is x= 5.


The function f(x) = x^3 + x^2 is monotonic, so there is NO other solution.


ANSWER.  The single and the unique solution to the problem is THIS : the length of the original cube is 5 inches.