If #(a^n + b^n)/(a^(n-1) + b^(n-1))# is the G.M between a & b find the value of'n'?
3 Answers
Explanation:
The geometric mean of
Thus,
#sqrt(ab)=(a^n+b^n)/(a^(n-1)+b^(n-1))#
Cross multiplying yields:
#(ab)^(1/2)(a^(n-1)+b^(n-1))=a^n+b^n#
#a^(n-1/2)b^(1/2)+a^(1/2)b^(n-1/2)=a^n+b^n#
#a^nsqrt(b/a)+b^nsqrt(a/b)=a^n+b^n#
Comparing coefficients, we see that
Explanation:
Putting
#(a^n+b^n)/(a^(n-1)+b^(n-1)) = (sqrt(a)+sqrt(b))/(1/sqrt(a)+1/sqrt(b))#
#color(white)((a^n+b^n)/(a^(n-1)+b^(n-1))) = (sqrt(a)+sqrt(b))/(((sqrt(a)+sqrt(b))/(sqrt(a)sqrt(b))))#
#color(white)((a^n+b^n)/(a^(n-1)+b^(n-1))) = sqrt(a)sqrt(b)#
#color(white)((a^n+b^n)/(a^(n-1)+b^(n-1))) = sqrt(ab)#
i.e. the geometric mean of
Explanation:
Assuming that G.M stands for geometric mean, we have
Now assuming