If x-3=3⅔+3⅓, then the value of x³-9x²+18x-10 is,
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Answer: 2
Explanation: x-3= 3⅔+3⅓.
cubing both sides
(x-3)³=(3⅔+3⅓)³.
x³-27-9x(x-3)=3²+3+3×3⅔×3⅓×(3⅔+3⅓).
x³-27-9x²+27x=12+9(x-3).
[3⅔+3⅓=x-3].
x³-27-9x²+27x=12+9x-27.
x³-27-9x²+27x-12-9x+27=0.
x³-9x²+18x-12=0.
adding 2 to both sides
x³-9x²+18x-12+2=0+2.
x³-9x²+18x-10=2.
Hence the answer is 2
Explanation: x-3= 3⅔+3⅓.
cubing both sides
(x-3)³=(3⅔+3⅓)³.
x³-27-9x(x-3)=3²+3+3×3⅔×3⅓×(3⅔+3⅓).
x³-27-9x²+27x=12+9(x-3).
[3⅔+3⅓=x-3].
x³-27-9x²+27x=12+9x-27.
x³-27-9x²+27x-12-9x+27=0.
x³-9x²+18x-12=0.
adding 2 to both sides
x³-9x²+18x-12+2=0+2.
x³-9x²+18x-10=2.
Hence the answer is 2
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