Question

If m = ³√15 and n = ³√14, find the value of
m-n-¹/m²+mn+n²​

Answer 1

Answer:0.0063

Step-by-step explanation:

Given that ,

m=cuberoot15

And. n=cuberoot14

To find: value of m-n^(-1)/m^2+mn+n^2

Here m=(15)^(3/2) & n=(14)^(3/2)

Now, consider N=(m-n^-1)=(15)^(3/2)-{1/(14)^(3/2)}

={(15×14)^(3/2)-1}/(14)^(3/2)

=(3043.189-1)/52.3832

N=58.0756

Now consider D=(m^2+mn+n^2)=(15)^3+(15×14)^(3/2)+(14)^3

=3375+3043.189+2744

D=9162.189

Now consider (N/D)=58.0756/9162.189

=0.0063