Question

The sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. their sum is: 20 30 40 none of these

Answer 1

let three numbers be x , y , z

according to first condition ,

x2 + y2 + z2 = 138 ------ ( 1 )

according to second condition ,

xy + yz + zx = 131 ------- ( 2 )

now ,
we know the identity

(x + y + z)^2 = x2 + y2 + z2 + 2xy + 2yz + 2zx

(x + y + z)^2 = x2 + y2 + z2 + 2(xy + yz + zx)

putting the values from 1 and 2 we get

(x + y + z)^2 = 138 + 2 × 131

(x + y + z)^2 = 138 + 262


(x + y + z)^2 = 400

taking square root of both sides

x + y + z = 20

so their sum is 20