Question

14) The Sum of Two number is 18. The sum of the squaries of numbers is 194. find the numbers​

Answer 1

5 and 13

Explanation:

given the first number is x and the second number is y

then x + y = 18 => y = 18 - x

also

x^2 + y^2 = 194

substitute

x^2 + (18 - x)^2 = 194

x^2 + x^2 - 36x + 324 = 194

2x^2 - 36x + 130 = 0

2(x^2 - 18x + 65) = 0

x^2 - 18x + 65 = 0/2

x^2 - 13x - 5x + 65 = 0

x(x - 13) - 5(x - 13) = 0

(x - 13)(x - 5) = 0

=> x - 13 = 0 => x = 13

=> x - 5 = 0 => x = 5

if x = 13, y = 18 - 13 = 5

if x = 5, y = 18 - 5 = 13

so x and y can be either 5 and 13