Sequence And Series Question 198
Question: If the arithmetic mean of two numbers be $ A $ and geometric mean be $ G $ , then the numbers will be
Options:
A) $ A\pm (A^{2}-G^{2}) $
B) $ \sqrt{A}\pm \sqrt{A^{2}-G^{2}} $
C) $ A\pm \sqrt{(A+G)(A-G)} $
D) $ \frac{A\pm \sqrt{(A+G)(A-G)}}{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
A.M. $ =\frac{a+b}{2}=A $ and G.M. $ =\sqrt{ab}=G $ On solving $ a $ and $ b $ are given by the values $ A\pm \sqrt{(A+G)(A-G)} $ . Trick: Let the numbers be 1, 9. Then $ A=5 $ and $ G=3 $ . Now put these values in options. Here (c)
$ \Rightarrow 5\pm \sqrt{8\times 2}\ i.e. $ 9 and 1.
BETA
