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Popular Word Problems >

the sum of two numbers is 9 and the sum of their squares is 41. find the two numbers

Solution

t h e s u m o f tw o n u mb ers i s 9 an d t h e s u m o f t h e i r s q u a res i s 41. f in d t h e tw o n u mb ers

Solution

The numbers : 4, 5

Solution steps

Represent the numbers with

x and y

:

number 1 : x

number 2 : y

A.T.Q.:

x + y = 9

x^{2} + y^{2} = 41

Solve the system of equations:

x + y = 9, x^{2} + y^{2} = 41 : (x = 4, x = 5, y = 5 y = 4)

Discard duplicated solutions

The numbers : 4, 5

Popular Examples

The difference between the squares of two consecutive integers is 29 twice a number is 500 more than six times the number four fifths of a number minus two is greater than three tenths of twice that number 54 is the difference between one half a number and 16 Seven times the larger of two numbers decreased by five times the smaller is 42 . Nine times the larger increased by 8 times the smaller is 256 . Find the numbers.