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Using (a–b)3 = a3–b3–3ab(a–b) tick the correct of these when x = p1/3 – p–1/3
- a)x3+3x = p + 1/p
- b)x3 + 3x = p – 1/p
- c)x3 + 3x = p + 1
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Using (a–b)3 = a3–b3–3ab(a–b) tick the correct...
Given: (ab)3 = a3b33ab(ab)
We need to find the correct option when x = p1/3
Substitute x = p1/3 in the given equation:
(a(p1/3)b)3 = a3b33a(p1/3)b(p1/3)(ab)
Simplify the equation:
a3p(b3)p = a3b33a(p1/3)b(p1/3)ab
a3p(b3)p = a3p(b3)p
Therefore, the equation is true for any value of a and b.
Now, let's check the given options:
a) x3 3x = p1/p
Substitute x = p1/3 in the option:
(p1/3)3 * 3(p1/3) = p1/p
p = p1/p
This equation is not true. Therefore, option (a) is incorrect.
b) x3 3x = p1/p
Substitute x = p1/3 in the option:
(p1/3)3 * 3(p1/3) = p1/3 * 3p1/3
p = p
This equation is true. Therefore, option (b) is correct.
c) x3 3x = p1/p
Substitute x = p1/3 in the option:
(p1/3)3 * 3(p1/3) = p1/2
This equation is not true. Therefore, option (c) is incorrect.
d) none of these
Option (b) is correct. Therefore, option (d) is incorrect.
Hence, the correct option is (b) x3 3x = p1/p.
We need to find the correct option when x = p1/3
Substitute x = p1/3 in the given equation:
(a(p1/3)b)3 = a3b33a(p1/3)b(p1/3)(ab)
Simplify the equation:
a3p(b3)p = a3b33a(p1/3)b(p1/3)ab
a3p(b3)p = a3p(b3)p
Therefore, the equation is true for any value of a and b.
Now, let's check the given options:
a) x3 3x = p1/p
Substitute x = p1/3 in the option:
(p1/3)3 * 3(p1/3) = p1/p
p = p1/p
This equation is not true. Therefore, option (a) is incorrect.
b) x3 3x = p1/p
Substitute x = p1/3 in the option:
(p1/3)3 * 3(p1/3) = p1/3 * 3p1/3
p = p
This equation is true. Therefore, option (b) is correct.
c) x3 3x = p1/p
Substitute x = p1/3 in the option:
(p1/3)3 * 3(p1/3) = p1/2
This equation is not true. Therefore, option (c) is incorrect.
d) none of these
Option (b) is correct. Therefore, option (d) is incorrect.
Hence, the correct option is (b) x3 3x = p1/p.
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Using (a–b)3 = a3–b3–3ab(a–b) tick the correct of these when x = p1/3 – p–1/3a)x3+3x = p + 1/pb)x3 + 3x = p – 1/pc)x3 + 3x = p + 1d)none of theseCorrect answer is option 'B'. Can you explain this answer?
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