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Popular Word Problems >

the sum of two numbers is 33 and the sum of their squares is 585. What is the smaller number

Solution

t h e s u m o f tw o n u mb ers i s 33 an d t h e s u m o f t h e i r s q u a res i s 585. Wha t i s t h e s ma ll er n u mb er

Solution

The smallest number : 12

Solution steps

Represent the numbers with

x and y

:

number 1 : x

number 2 : y

A.T.Q.:

x + y = 33

x^{2} + y^{2} = 585

Solve the system of equations:

x + y = 33, x^{2} + y^{2} = 585 : (x = 12, x = 21, y = 21 y = 12)

Discard duplicated solutions

Select the smallest solution:

12

The smallest number : 12

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