Question

If P, Q be the A.M., G.M. respectively between any two rational numbers a and b, then P – Q is equal

to​

Answer 1

Answer:

If P,Q be the A.M., G.M. respectively between any two rational numbers a and b, then P-Q is equal to. (A) a-ba (B) a+b2 (C) 2aba+b (D) (√a-√b√2)2.

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Answer 2

$\displaystyle \bf P - Q = {\bigg( \frac{ \sqrt{a} - \sqrt{b} }{ \sqrt{2} } \bigg)}^{2}$

Given :

P, Q be the A.M., G.M. respectively between any two rational numbers a and b

To find :

The value of P - Q

Solution :

Step 1 of 2 :

Find the value of a and b

Here it is given that P, Q be the A.M. , G.M. respectively between any two rational numbers a and b

$\displaystyle \sf P = \frac{a + b}{2}$

$\displaystyle \sf Q = \sqrt{ab}$

Step 2 of 2 :

Find the value of P - Q

$\displaystyle \sf P - Q$

$\displaystyle \sf = \frac{a + b}{2} - \sqrt{ab}$

$\displaystyle \sf = \frac{a + b - 2 \sqrt{ab} }{2}$

$\displaystyle \sf = \frac{ {( \sqrt{a} )}^{2} + {( \sqrt{b} )}^{2} - 2 \sqrt{a}. \sqrt{b} }{ {( \sqrt{2} )}^{2} }$

$\displaystyle \sf = {\bigg( \frac{ \sqrt{a} - \sqrt{b} }{ \sqrt{2} } \bigg)}^{2}$

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