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  • The sum of three number is 10 and the sum of their square is 38 then find the sum of the product of the three numbers taking two at a time​

The sum of three number is 10 and the sum of their square is 38 then find the sum of the product of the three numbers taking two at a time​

Answers (1)

best_answer

 let the numbers are a,b,c respectively

So according to the question

a+b+c=10

and

a^2+b^2+c^2=38

Now we want to find out

 the sum of the product of the three numbers taking two at a time

i.e ab+bc+ca=x= ?

So using

(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)\\\Rightarrow (10)^2=38+2x\\ \Rightarrow 100=38+2x\\ \Rightarrow x=\frac{100-38}{2}=\frac{62}{2}=31

Posted by

avinash.dongre

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