Question

The sum of two numbers is 9 and the sum of their squares is 41. Taking one number as x, form ail equation in x and solve it to find the numbers.

Answer 1

Sum of two numbers = 9
Let first number = x
then second number = 9 – x
Now according to the condition,
(x)² + (9 - x)² = 41
⇒ x² + 81 - 18x + x² - 41 = 0
⇒ 2x² - 18x + 40 = 0
⇒ x² - 9x + 20 = 0    ...(Dividing by 2)
⇒ x² - 4x - 5x + 20 = 0
⇒ (x - 4) -5(x - 4) = 0
⇒ (x - 4) (x - 5) = 0
Either x - 4 = 0,
then x = 4
or
x - 5 = 0, 
then x = 5
(i) If x = 4, then first number = 4
and second number = 9 - 4 = 5
(ii) If x = 5, then first number = 5
ans second number = 9 - 5 = 4
Hence numbers are 4 and 5.