Question

No Spam. I will mark Brainliest, if you get it right. A tank's length is 4 feet longer than its width. The height is 2 feet more than the width. The volume of the tank is 105 cubic feet. What is the width of the tank?

Answer 1

Answer: 3

Step-by-step explanation:

Let say x the width of the tank,

x+4 its length,

x+2 its height

$Volume=105=x(x+4)(x+2)\\\\P(x)=x^3+6x^2+8x-105=0\\\\105=3*5*7\\\\P(1)\neq 0\\P(-1)\neq 0\\P(3)=0\\\\\begin{array}{|c|cccc|}&x^3&x^2&x&1\\&1&6&8&-105\\x=3&&3&27&105\\----&--&--&--&--\\&1&9&35&0\\\end{array}\\\\\\P(x)=x^3+6x^2+8x-105=(x-3)(x^2+9x+35)\\And \ x^2+9x+35\ is\ not \ factorizable\ (\Delat=9^2-4*35 < 0)$

width=3

length=3+4=7

height=3+2=5