Question : The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, then the sum of the squares of the numbers is:
Option 1: 120
Option 2: 126
Option 3: 132
Option 4: 138

Question

Question : The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, then the sum of the squares of the numbers is:

Option 1: 120

Option 2: 126

Option 3: 132

Option 4: 138

Team Careers360 · Accepted Answer

Correct Answer: 126

Solution : Let three numbers be $a, b$ and $c$.
Given: $a + b + c = 18, a + b = c$ and $abc = 162$
Put $a + b = c$ in $a + b + c = 18$
$2c = 18$
⇒ $c = 9 = a + b$ ---(1)
$ab × 9 = 162$
⇒ $ab = \frac{162}{9}$
⇒ $ab = 18 $ ---(2)
From (1) and (2) we get,
⇒ $a=6, b=3$
So, the sum of the squares of the numbers
= $(a^{2}+b^{2}+c^{2}) = (6^{2}+3^{2}+9^{2})= (36+9+81)= 126$
Hence, the correct answer is 126.

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Question : The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, then the sum of the squares of the numbers is:Option 1: 120Option 2: 126Option 3: 132Option 4: 138

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Question : The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, then the sum of the squares of the numbers is:
Option 1: 120
Option 2: 126
Option 3: 132
Option 4: 138