Question

If x=2 – 2 1/3 +2 2/3, then the value of x3-6x2+18x+18 is

Answer 1

x=2-2 1/3+2 2/3
2 1/3=(2×3+1)/3=7/3
2 2/3=(2×3+2)/3=8/3
x=2-7/3+8/3
x=2-1/3
x=5/3
now, x3-6x2+18x+18=
(5/3)^3-(6×(5/3)^2)+18×(5/3)+18
(125/27)-(50/3)+30+18
(125/27)-(450/27)+48
(-325/27)+48
(48×27-325)/27
971/27
or 35.96

Answer 2

The Value of  $x^{3} -6x^{2} +18x+18=\frac{971}{27}$

Step-by-step explanation:

Given:-

$x=2-2\frac{1}{3}+2\frac{2}{3}$

$x=2-(\frac{(2\times3)+1}{3} )+(\frac{(2\times3)+2}{3} )$

$x=2-(\frac{6+1}{3} )+(\frac{6+2}{3} )$

$x=2-\frac{7}{3} +\frac{8}{3}$

$x=2-(\frac{8-7}{3} )$

$x=2-\frac{1}{3}$

$x=\frac{6-1}{3}$

$\therefore\ x=\frac{5}{3}$  ---------------------(equation 1)

To find:-

$x^{3}-6x^{2} +18x+18= ?$

Solution:-

Now substituting the value of x from equation 1 in below equation

$x^{3}-6x^{2} +18x+18= ?$

$=(\frac{5}{3} )^{3} -(6\times (\frac{5}{3})^{2}) +(18\times \frac{5}{3}) +18$

$= \frac{125}{27} -(\frac{6\times 25}{9}) +(\frac{18\ties 5}{3}) +18$

$=\frac{125}{27} -\frac{150}{9}+\frac{90}{3} +18$

$=(\frac{125-450}{27}) +30+18$

$=\frac{-325}{27} +48$

$=\frac{-325+(48\times27)}{27}$

$=\frac{-325+1296}{27}$

$=\frac{971}{27}$

$\therefore\ x^{3} -6x^{2} +18x+18=\frac{971}{27}$