MCQ
If p, q be two A.M.'s and G be one G.M. between two numbers, then G2 =
- A$(2\text{p}-\text{q})(\text{p}-2\text{q})$
- B$(2\text{p}-\text{q})(2\text{q}-\text{p})$
- C$(2\text{p}-\text{q})(\text{p}+2\text{q})$
- DNone of these.
Solution:
Let the two numbers be a and b.
a, p, q and b are in A.P.
$\therefore\text{ p}-\text{a}=\text{q}-\text{q}=\text{b}-\text{q}$
$\Rightarrow\text{ p}-\text{a}=\text{q}-\text{p}\text{ and}\text{ q}-\text{p}=\text{b}-\text{q}$
$\Rightarrow\text{ a}=2\text{p}-\text{q}\text{ and}\text{ b}=2\text{q}-\text{p}\cdots(\text{i})$
Also, a, G and b are in G.P.
$\therefore\text{G}^2=\text{ab}$
$\Rightarrow\text{G}^2=(2\text{p}-\text{q})(2\text{q}-\text{p})$
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Domain of $\sqrt{\text{a}^2-\text{x}^2}(\text{a}>0)$ is.