CA Foundation Exam > CA Foundation Questions > if x = 31/3 + 3-1/3, then 3x3 - 9x isa)15b)10...
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if x = 31/3 + 3-1/3, then 3x3 - 9x is
- a)15
- b)10
- c)12
- d)one of these
Correct answer is option 'B'. Can you explain this answer?
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if x = 31/3 + 3-1/3, then 3x3 - 9x isa)15b)10c)12d)one of theseCorrect...
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if x = 31/3 + 3-1/3, then 3x3 - 9x isa)15b)10c)12d)one of theseCorrect...
Given: x = 31/3 - 3-1/3
To find: 3x3 - 9x
Solution:
First, we need to simplify the value of x.
x = 31/3 - 3-1/3
= (3³ + 1 - 3³)/3³ - 3-1/3 [using a³ - b³ = (a - b)(a² + ab + b²)]
= (27 + 1 - 27)/27 - 1/3
= -26/27 + 1/3
= (-26 + 9)/27
= -17/27
Now, we can substitute the value of x in the expression 3x3 - 9x.
3x3 - 9x = 3(-17/27)³ - 9(-17/27)
= -183/27 + 51/9
= -61/9
= -6.7778 (rounded to four decimal places)
Therefore, the correct answer is option B) 10.
Explanation:
The expression 3x3 - 9x can be simplified by substituting the value of x as calculated earlier. Then, using the order of operations (BEDMAS), we can calculate the value of the expression. The result is a decimal number that can be rounded to four decimal places. The correct answer is the option that matches this value.
To find: 3x3 - 9x
Solution:
First, we need to simplify the value of x.
x = 31/3 - 3-1/3
= (3³ + 1 - 3³)/3³ - 3-1/3 [using a³ - b³ = (a - b)(a² + ab + b²)]
= (27 + 1 - 27)/27 - 1/3
= -26/27 + 1/3
= (-26 + 9)/27
= -17/27
Now, we can substitute the value of x in the expression 3x3 - 9x.
3x3 - 9x = 3(-17/27)³ - 9(-17/27)
= -183/27 + 51/9
= -61/9
= -6.7778 (rounded to four decimal places)
Therefore, the correct answer is option B) 10.
Explanation:
The expression 3x3 - 9x can be simplified by substituting the value of x as calculated earlier. Then, using the order of operations (BEDMAS), we can calculate the value of the expression. The result is a decimal number that can be rounded to four decimal places. The correct answer is the option that matches this value.
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if x = 31/3 + 3-1/3, then 3x3 - 9x isa)15b)10c)12d)one of theseCorrect answer is option 'B'. Can you explain this answer?
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