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Popular Word Problems >

the difference of two numbers is equal to 6. moreover, the square of the sum of these numbers is 441. find these numbers

Solution

t h e d i ff ere n ce o f tw o n u mb ers i s e q u a l t o 6. m oreo v er, t h e s q u a re o f t h e s u m o f t h ese n u mb ers i s 441. f in d t h ese n u mb ers

Solution

The numbers : 441 - \frac{441 - 6}{2}, \frac{441 - 6}{2} or 441 - \frac{441 + 6}{2}, \frac{441 + 6}{2}

Solution steps

Represent the numbers with

x and y

:

number 1 : x

number 2 : y

A.T.Q.:

(x - y)^{2} = 6

x + y = 441

Solve the system of equations:

(x - y)^{2} = 6, x + y = 441 : (x = 441 - \frac{441 - 6}{2}, x = 441 - \frac{441 + 6}{2}, y = \frac{441 - 6}{2} y = \frac{441 + 6}{2})

The numbers : 441 - \frac{441 - 6}{2}, \frac{441 - 6}{2} or 441 - \frac{441 + 6}{2}, \frac{441 + 6}{2}

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