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, the sum of the squares of the numbers is:
Option 1: 120
Option 2: 126
Option 3: 132
Option 4: 138
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Correct Answer: 126
Solution : Let the three positive numbers be $x, y,$ and $z$. The sum of three positive numbers, $x + y + z = 18$--------- (1) The product of the three numbers, $x × y × z = 162$---------------------- (2) Given that the sum of two numbers is equal to the third. i.e., $x + y = z$ ⇒ $2z = 18$ ⇒ $z = 9$ Replacing $z = 9$ in equations (1) and (2), We get $x + y = 9$ and $x × y = 18$ $⇒x = 6$ and $y = 3$ Therefore, the sum of squares of the numbers = 6 2 + 3 2 + 9 2 = 36 + 9 + 81 = 126 Hence, the correct answer is 126.
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