Question

sum of two numbers is 18 and sum of their squares is 190 find the 2 numbers?

Answer should be done by
@teneetiraj86

Answer 1

Answer:

Step-by-step explanation:

the two numbers are 9+√14 and 9-√14

Check:+

Their sum=9+√14+9-√14=9+9=18

Sum of their squares=

(9+√14)²+(9-√14)²

=81+14+18√14+81+14-18√14

=81+14+81+14

=95+95

=190

Verified

Answer 2

Answer :-

• Two numbers are 7 and 11 respectively.

Given :-

• Sum of two numbers is 18 and sum of their squares is 170.

To Find :-

• Those two numbers.

Solution :-

Let

• First number be x
• Second number will be (18 - x)

On squaring

• First number = x²
• Second number = (18 - x)²

It is given that

• Sum of their squares is 190.

According to question :-

⇒ x² + (18 - x)² = 170

⇒ x² + (18)² + (x)² - 2.18.x = 170

⇒ x² + 324 + x² - 36x = 170

⇒ 2x² - 36x + 324 = 170

⇒ 2x² - 36x + 324 - 170

⇒ 2x² - 36x + 154 = 0

⇒ x² - 18x + 77 = 0

⇒ x² - 11x - 7x + 77 = 0

⇒ x (x - 11) - 7 (x - 11)

⇒ x = 7,11

Hence, the two numbers are 7 and 11 respectively.