Question 1117630
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The coefficient of the x^2 term in {{{(2x+k)^6}}} is {{{C(6,2)*(2^2)*(k^4)}}}<br>
The coefficient of the x^5 term in {{{(2+kx)^8}}} is {{{C(8,5)*(k^5)*(2^3)}}}<br>
{{{C(6,2)*(2^2)*(k^4) = C(8,5)*(k^5)*(2^3)}}}<br>
{{{15*4*k^4 = 56*8*k^5}}}
{{{60k^4 = 448k^5}}}
{{{k = 60/448 = 15/112}}}<br>
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.