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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


Team Careers360 13th Jan, 2024
Answer (1)
Team Careers360 25th Jan, 2024

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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