If a+b+c=9 and ab+bc+ac=26,finda^2+b^2+c^2
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ab + bc + ca = 26 -----(1)
a + b + c = 9
On squaring both sides, we get
( a + b +c)^2 = 9^2
=> a^2 + b^2 + c^2 + 2ab + 2bc +2ca = 81
=> a^2 + b^2 + c^2 + 2 ( ab + bc + ca) = 81
=> a^2 + b^2 + c^2 + 2 ( 26) = 81
=> a^2 + b^2 + c^2 + 52 = 81
=> a^2 + b^2 + c^2 = 29
a + b + c = 9
On squaring both sides, we get
( a + b +c)^2 = 9^2
=> a^2 + b^2 + c^2 + 2ab + 2bc +2ca = 81
=> a^2 + b^2 + c^2 + 2 ( ab + bc + ca) = 81
=> a^2 + b^2 + c^2 + 2 ( 26) = 81
=> a^2 + b^2 + c^2 + 52 = 81
=> a^2 + b^2 + c^2 = 29
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