Question : The sum of the squares of three positive numbers is 323. If the sum of the squares of two numbers is twice the third, their product is:
Option 1: 255
Option 2: 260
Option 3: 275
Option 4: 270
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Correct Answer: 255
Solution :
Let the three numbers be a, b and c.
According to the question,
a
2
+ b
2
+ c
2
= 323 and a
2
+ b
2
= 2c
⇒ c
2
+ 2c = 323
⇒ c
2
+ 2c – 323 = 0
⇒ (c + 19) (c – 17) = 0
Taking, c = 17 as c can't be negative.
⇒ a
2
+ b
2
= 2c
⇒ a
2
+ b
2
= 2 × 17
⇒ a
2
+ b
2
= 34
⇒ a
2
+ b
2
= 25 + 9
⇒ a
2
+ b
2
= 5
2
+ 3
2
Comparing both sides we get, a = 5 and b = 3 (taking a > b)
So, the product of a, b, and c = 3 × 5 × 17 = 255
Hence, the correct answer is 255.
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