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Popular Word Problems >

Find two consecutive integers such that the square of the larger integer is ninteen more than nine times the smaller integer

Solution

solve for

tw o co n sec u t i v e in t e g ers s u c h t ha t t h e s q u a re o f t h e l a r g er in t e g er i s nin t ee n m ore t han nin e t im es t h e s ma ll er in t e g er

Solution

The numbers : 9, 10 or - 2, - 1

Solution steps

Represent the numbers with

x

:

First number : x

Consecutive number : x + 1

A.T.Q.:

(x + 1)^{2} = 19 + 9 x

Solve

(x + 1)^{2} = 19 + 9 x : x = 9, x = - 2

Plug in

x = 9 : 10

Plug in

x = - 2 : - 1

The numbers : 9, 10 or - 2, - 1

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