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Popular Word Problems >

One positive integer is 6 less than twice another. The sum of their squares is 164. Find the integers.

Solution

O n e p os i t i v e in t e g er i s 6 l ess t han tw i ce an o t h er . T h e s u m o f t h e i r s q u a res i s 164. F in d t h e in t e g ers .

Solution

The numbers : 10, 8

Solution steps

Represent the numbers with

x and y

:

number 1 : x

number 2 : y

A.T.Q.:

x = 2 y - 6

x^{2} + y^{2} = 164

Solve the system of equations:

x = 2 y - 6, x^{2} + y^{2} = 164 : (x = 10, x = - \frac{62}{5}, y = 8 y = - \frac{16}{5})

Select positive solutions:

8, 10

The numbers : 10, 8

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