Question

The sum of the squares of two consecutive integers is 85. Find the integers.

Answer 1

you know what consecutive integers are ?

Answer 2

yeah.

Answer 3

x^2+y^2=85. since you know they are consecutive, y must be 1 greater than x. so y=x+1. plug and play

Answer 4

or initially you can take 2 numbers as x and x+1
and get
x^2 + (x+1)^2 = 85 directly
can you slve this quadratic ?

Answer 5

then it would be 2x^2 + 2x - 84 = 0

Answer 6

yes
which is
x^2+x-42 =0
can you factor ?
2 numbers with sum = 1 , product = -42 ?

Answer 7

(x + 7) (x - 6) am i right?

Answer 8

yes!

Answer 9

i think you'll now get those 2 numbers :)

Answer 10

so which will be the x then? will it be -7 or 6?

Answer 11

both!

-7, -7+1 -----> -7,-6

6, 6+1 ------> 6,7
:)

Answer 12

okay. thanks :)

Answer 13

welcome ^_^