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The average of two numbers is 6.5 and square root of their product is 6. What are the numbers?
Answer & Solution
Correct Answer:
Option
C
Let the two numbers be x and y
Then,
x + y = 6.5 × 2 = 13 and
$$\sqrt {{\text{xy}}} $$ = 6 or xy = 36
⇒ (x - y)2 = (x + y)2 - 4xy
⇒ (x - y)2 = (13)2 - 4 × 36
⇒ (x - y)2 = 169 - 144
⇒ (x - y)2 = 25
⇒ (x - y) = 5
Solving x + y = 13 and x - y = 5
We get : x = 9 , y = 4
Then,
x + y = 6.5 × 2 = 13 and
$$\sqrt {{\text{xy}}} $$ = 6 or xy = 36
⇒ (x - y)2 = (x + y)2 - 4xy
⇒ (x - y)2 = (13)2 - 4 × 36
⇒ (x - y)2 = 169 - 144
⇒ (x - y)2 = 25
⇒ (x - y) = 5
Solving x + y = 13 and x - y = 5
We get : x = 9 , y = 4
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