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If x=3+3^2/3+3^1/3,then the value of x^3-9x^2+18x-12 =

If x=3+3^2/3+3^1/3,then the value of x^3-9x^2+18x-12 =

Grade:12th pass

3 Answers

Ritesh Khatri
76 Points
6 years ago
x – 3 = 3^2/3 + 3^1/3
(x – 3)^3 = (3^2/3 + 3^1/3)^3
x^3 – 27 + 27x – 9x^2 = 9 + 3 + 3*3^2/3*3^1/3(3^2/3 + 3^1/3)
x^3 – 27 + 27x – 9x^2 = 12 + 9( x – 3)
x^3 – 9x^2 + 18x – 27 = 12 – 27
x^3 – 9x^2 + 18x – 12 = 0
Shailendra Kumar Sharma
188 Points
6 years ago
Take x = 3+ 3^(1/3)+3^(2/3)If we are (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3This way it can be seen if we multiply 3^(1/3) with 3^(2/3) give 3So take the x-3 = 3^(1/3)+3^(2/3)Cube both side x3+27x-9x2-27 = 3+9+3*3^(5/3)+ 3*3^(4/3)=> x^3 – 27 + 27x – 9x^2 = 12 + 9( x – 3)=> x^3 – 9x^2 + 18x – 27 = 12 – 27=> x^3 – 9x^2 + 18x – 12 = 0
Manisha
15 Points
5 years ago
X/3+1=5/3
Y-2/3=1/3
X+3 = 5            3y-2     = 1
_____  _____ ; ________     ___
3          3               3            3
x+3=5 ; 3y-2=1
x=5-3 ; 3y=1+2
x=2 ; 3y=3
x=2 ; y=3/3
x=2 ; y=1
 

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