Explanation
We are given:
u+f=(2+1)10
v=(2−1)10
We need to find the product uv. First, let us look at the product of the base expressions:
(2+1)(2−1)=(2)2−(1)2=2−1=1
Now, consider the product of the terms:
(u+f)v=(2+1)10×(2−1)10
(u+f)v=[(2+1)(2−1)]10
(u+f)v=(1)10=1
Expanding the left side:
uv+fv=1
uv=1−fv
Since 0 < f < 1 and 0 < v < 1, the product fv must be a positive value between 0 and 1 (i.e., 0 < fv < 1).
Substituting this into the equation uv=1−fv:
If 0 < fv < 1, then 1 - 1 < 1 - fv < 1 - 0.
Therefore, 0 < uv < 1.
Conclusion: The product uv lies between 0 and 1.
Correct Option: (c) 0 < uv < 1
