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If (a+b+c)= 8 and (ab + bc + ac)= 19 find (a2 + b2 +c2)
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If (a+b+c)= 8 and (ab + bc + ac)= 19 find (a2 + b2 +c2)
Calculation of (a2 b2 c2) given (a b c)=8 and (ab bc ac)=19


Given


  • (a b c)=8

  • (ab bc ac)=19



Approach

Since we know that:


  • (a+b+c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ac

  • (a+b+c)2 = a2 + b2 + c2 + 2(ab + bc + ac)


So, we can calculate (a2 + b2 + c2) as:


  • a2 + b2 + c2 = (a+b+c)2 - 2(ab + bc + ac)



Calculation

Using the above equation, we can calculate (a2 + b2 + c2) as:


  • a2 + b2 + c2 = (a+b+c)2 - 2(ab + bc + ac)

  • a2 + b2 + c2 = 82 - 2(19)

  • a2 + b2 + c2 = 64 - 38

  • a2 + b2 + c2 = 26



Answer

Therefore, (a2 + b2 + c2) = 26.
Community Answer
If (a+b+c)= 8 and (ab + bc + ac)= 19 find (a2 + b2 +c2)
a2+b2+c2= 26solutions (a+b+c)2 =a2+b2+c2+2 (a+b+c)(8)2=a2+b2+c2+2 (19)64=a2+b2+c2+3864-38=a2+b2+c226=a2+b2+c2
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If (a+b+c)= 8 and (ab + bc + ac)= 19 find (a2 + b2 +c2)
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