Question

The sum of squares of three numbers is 138 and the sum of their

products takn two at a time is 131. Find their sum?​

Answer 1

Answer:

Sum of numbers = 20

Step-by-step explanation:

Let a , b & c , be the three numbers , then :

According to question ;

a² + b² + c² = 138 — equation ( 1 )

Also ,

( ab + bc + ca ) = 131

Now , by multiplying above equation by 2 on both side , we get ;

2 ( ab + bc + ca ) = 2 ( 131 ) = 262 — equation ( 2 )

Adding equations ( 1 ) & ( 2 ) , we get ;

a² + b² + c² + 2 ( ab + bc + ca ) = 138 + 262

( a + b + c )² = 400 ( by identity )

a + b + c = 20 ( taking square root on both side )

Hence , sum of numbers is 20

Glad to help you , you can follow me to get best solutions for your every doubt .