Question

There is a natural number that becomes equal to the square of a natural number when 100 is added to it and to the square of another natural number when 169 is added to it .Find the number?

Answer 1

x+100=n^2
x+169 = m^2

Answer 2

x + 100 = y^2
x + 169 = z^2

Answer 3

diphontane equation

Answer 4

subtract
z^2 - y^2 = 69
(z + y)(z - y) = 69

can you continue?

Answer 5

x y and z are all natural numbers

Answer 6

13,10.....?

Answer 7

23.3

Answer 8

z + y =23
z - y = 3

is a possibility

Answer 9

http://www.wolframalpha.com/input/?i=n^2-m^2%3D69&dataset=&equal=Submit

Answer 10

do i have to guess the answer?

Answer 11

no

try and fit those numbers to the 2 equations

Answer 12

solve the 2 simultaneous equations first

Answer 13

z=13
y=10

Answer 14

yep

Answer 15

now work out value of x

Answer 16

how?

Answer 17

from the original equations

Answer 18

the other possibility is
y + z= 69
y - z = 1

Answer 19

x + 100 = 10^2

x = 0

now to be honest I cant remember if 0 is a natural number

Answer 20

y=35
z=34

Answer 21

you can do the same processing for
z + y = 69
z - y = 1

this gives z = 35 y = 34

Answer 22

925..?

Answer 23

giving x = 34^2 - 100

Answer 24

1056

Answer 25

sorry one of my last posts was incorrect

its z - y = 1 not y - z = 1

Answer 26

there are 2 possibilities for

(z + y)(z - y) = 69 if z and y are natural numbers

the left hand side is either 23*3 or 69 * 1