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 then the sum of squares of the numbers isSolution
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
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