SOLUTION: the coefficient of x^2 in the expansion of (2x+k)^6 is equal to the coefficient of x^5 in the expansion of (2+kx)^8. find k

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Question 1117630: the coefficient of x^2 in the expansion of (2x+k)^6 is equal to the coefficient of x^5 in the expansion of (2+kx)^8. find k
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The coefficient of the x^2 term in %282x%2Bk%29%5E6 is C%286%2C2%29%2A%282%5E2%29%2A%28k%5E4%29

The coefficient of the x^5 term in %282%2Bkx%29%5E8 is C%288%2C5%29%2A%28k%5E5%29%2A%282%5E3%29

C%286%2C2%29%2A%282%5E2%29%2A%28k%5E4%29+=+C%288%2C5%29%2A%28k%5E5%29%2A%282%5E3%29

15%2A4%2Ak%5E4+=+56%2A8%2Ak%5E5
60k%5E4+=+448k%5E5
k+=+60%2F448+=+15%2F112

When I got this "ugly" answer, I guessed that there was an error in your statement of the problem. However, wolframalpha.com confirmed that this value of k does indeed make the two coefficients equal.