Question

if the sum of 2 numbers is 18 and the sum of their squares is 290 find the number ​

Answer 1

Step-by-step explanation:

x + y = 18

x² + y² = 290

...from first equation:

x = 18 – y

...substitute that into second equation:

(18 – y)² + y² = 290

324 – 36y + y² + y² = 290

2y² – 36y + 34 = 0

y² – 18y + 17 = 0

(y – 1)(y – 17) = 0

y = 1 or 17

y = 1 ⇒ x = 17

y = 17 ⇒ x = 1

The numbers are 1 and 17.

Check:

x + y = 18 → 1 + 17 = 18

x² + y² = 290 → 1² + 17² = 1 + 289 = 290

Answer 2

Answer:

x + y = 18

x² + y² = 290

...from first equation:

x = 18 – y

...substitute that into second equation:

(18 – y)² + y² = 290

324 – 36y + y² + y² = 290

2y² – 36y + 34 = 0

y² – 18y + 17 = 0

(y – 1)(y – 17) = 0

y = 1 or 17

y = 1 ⇒ x = 17

y = 17 ⇒ x = 1

The numbers are 1 and 17.

Check:

x + y = 18 → 1 + 17 = 18

x² + y² = 290 → 1² + 17² = 1 + 289 = 290