Question

The sum of the squares of 3 numbers is 170. While the sum of their products taken two at a line is 157. What is the sum of the numbers?

Answer 1

use the identity of (a+b+c)(a+b+c)

Answer 2

Answer:

The sum of numbers is 22

Step-by-step explanation:

Given the sum of the squares of 3 numbers is 170 while the sum of their products taken two at a line is 157. we have to find the sum of the numbers.

Let the three numbers are a, b and c

The sum of the squares of 3 numbers is 170 ⇒ $a^{2}+b^{2}+c^{2}=170$

The sum of their products taken two at time is 157

⇒ $ab+bc+ca=157$

Applying the identity,

$(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2ab+2bc+2ca$

⇒ $(a+b+c)^{2}=170+2(ab+bc+ca)$

⇒  $(a+b+c)^{2}=170+2(157)$

⇒  $(a+b+c)^{2}=484$

⇒  $(a+b+c)=\sqrt{484}$ ⇒ (a+b+c)=22

Hence, the sum of numbers is 22