Q. 304.0( 6 Votes )

If π‘Ž + 𝑏 + 𝑐 = 9 and π‘Žπ‘ + 𝑏𝑐 + π‘π‘Ž = 26, find π‘Ž2 + 𝑏2 + 𝑐2.

Answer :

Given that: a + b + c = 9 and π‘Žπ‘ + 𝑏𝑐 + π‘π‘Ž = 26

Using the identity (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca, we have(9)2 = a2 + b2 + c2 + 2(ab + bc + ca)


⟹ 81 = a2 + b2 + c2 + 2(26)


⟹ 81 = a2 + b2 + c2 + 52


⟹ 81 βˆ’ 52 = a2 + b2 + c2


⟹ a2 + b2 + c2= 29


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