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If (1 + ax)n = 1 + 8x + 24x2 + ….., then the values of a and n are equal to
- a)2, 4
- b)2, 3
- c)3, 6
- d)1, 2
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If (1 + ax)n = 1 + 8x + 24x2 + ….., then the values of a and n ...
∴ n = 4,a = 2
Most Upvoted Answer
If (1 + ax)n = 1 + 8x + 24x2 + ….., then the values of a and n ...
∴ n = 4,a = 2
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If (1 + ax)n = 1 + 8x + 24x2 + ….., then the values of a and n ...
Explanation:
Given Equation:
(1 + ax)^n = 1 + 8x + 24x^2 + ...
Expanding the equation:
Using binomial theorem, we can expand the given equation as follows:
(1 + ax)^n = 1 + n(ax) + n(n-1)(ax)^2/2! + ...
Comparing coefficients:
- Constant term: 1 = 1
- Coefficient of x: 8x = n(ax)
- Coefficient of x^2: 24x^2 = n(n-1)(ax)^2/2!
Calculating the values:
From the coefficient of x, we get: n = 8/a
Substitute n in the coefficient of x^2 equation:
24x^2 = (8/a)(7/a)(a^2x^2)/2
Solving this, we get: a = 2, n = 4
Therefore, the values of a and n are 2 and 4 respectively, which matches with option A.
Given Equation:
(1 + ax)^n = 1 + 8x + 24x^2 + ...
Expanding the equation:
Using binomial theorem, we can expand the given equation as follows:
(1 + ax)^n = 1 + n(ax) + n(n-1)(ax)^2/2! + ...
Comparing coefficients:
- Constant term: 1 = 1
- Coefficient of x: 8x = n(ax)
- Coefficient of x^2: 24x^2 = n(n-1)(ax)^2/2!
Calculating the values:
From the coefficient of x, we get: n = 8/a
Substitute n in the coefficient of x^2 equation:
24x^2 = (8/a)(7/a)(a^2x^2)/2
Solving this, we get: a = 2, n = 4
Therefore, the values of a and n are 2 and 4 respectively, which matches with option A.
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