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:

A. 20

B. 30

C. 40

D. None of these


Option A. 20 is the right answer

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Let suppose The sum of the squares of three numbers is 138 i.e
  a2 + b2 + c2 = 138
And, the sum of their products taken two at a time is 131 i.e
(ab + bc + ca) = 131
Now, as we know that
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
By putting the values, we get
(a + b + c)2 = 138 + 2 x 131
(a + b + c)2 =   400
By taking under root on both sides, we get
(a + b + c)2 =   400

(a + b + c)  = 20

Hence, if the sum of the squares of three numbers is 138, while the sum of their products taken two at a time is 131. Thenm their sum is 20 as proved above.

which is our right answer:)


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