SOLUTION: Use quadratic formula and a calculator to solve. Round decimal approximations to the nearest hundredth. Find two integers such that the larger is 2 less than eight times the sm

Question 1029358: Use quadratic formula and a calculator to solve. Round decimal approximations to the nearest hundredth.
Find two integers such that the larger is 2 less than eight times the smaller and the difference of their squares is 884
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
let a = the larger number
let b = the smaller number

a = 8b-2

this means that the larger number is 2 less than 8 times the smaller number.

a^2 - b^2 = 884.

this means that difference between the squares of each of the numbers is 884.

replace a^2 with (8b-2)^2 in the second equation to get:

(8b-2)^2 - b^2 = 884

simplify to get 64b^2 - 32b + 4 - b^2 = 884

combine like terms to get 63b^2 - 32b + 4 = 884

subtract 884 from both sides of this equation to get 63b^2 - 32b - 880 = 0

use the quadratic formula to get:

b = - 3.492063... or b = 4

the integer you are looking for is 4.

that's the smaller number

a = 8b-2 makes a = 30

that's the larger number.

a^2 - b^2 becomes (30)^2 - (4)^2 = 884.

the requirements are satisfied.

the larger number is 30.
the smaller number is 4.

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