The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third then the sum of squares of the numbers is
Show answer & explanation
Correct answer: B
Explanation
The correct option is 2.
Let us consider the three positive numbers as x,y and z.
Sum of three positive numbers x + y + z = 18 ---------> (1)
product of three numbers xyz = 162 ----------> (2)
Given that sum of two numbers is equal to the third. i.e.., x + y = z
=> 2z = 18
=> z = 9
replacing z = 9 in equation (1) & (2), we get x + y = 9 and xy = 18
Solving above, we get x = 6 and y = 3
therefore, sum of squares of the numbers = 62 + 32 + 92 = 126