Question 8

The sum of three positive numbersis 18 and their product is 162. If the sum of two numbersis equal to the third then the sum of squares of the numbersis

Solution

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 = $$ 6^2+3^2+9^2$$=126

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