Question

if the sum of two numbers is 18 and sum their square is164 then the smallest number is​

Answer 1

$\huge{ \red{ \bf solution : }}$

Let the two numbers be x and y.

According to given condition,

x + y = 18

=> x = 18 - y ...(i)

x² + y² = 164...(ii)

Substitute (i) in eqⁿ (ii)

x² + y² = 164

⇒ (18 - y)² + y² = 164

⇒ 324 + y² - 36y + y² = 164

⇒ 2y² - 36y + 324 - 164 = 0

⇒ 2y² - 36y + 160 = 0

⇒ 2 (y² - 18y + 80) = 0

⇒ y² - 18y + 80 = 0

⇒ y² - 10y - 8y + 80 = 0

⇒ y ( y - 10 ) - 8 ( y - 10 ) = 0

⇒ ( y - 10 ) ( y - 8 ) = 0

⇒ y = 10 or y = 8

Therefore, numbers are 10 and 8.

Smallest number = 8