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If a+b+c = 9 and ab+bc+ca = 40, find a^2 + b^2 + c^2

If Abc 9 And Abbcca 40 Find A2 B2 C2 class=

Sagot :

[tex]a^2+b^2+c^2=1[/tex]

Explanation

By definition.

[tex]\begin{gathered} (a+b+c)^2=a^2+b^2+c^2+2((ab)+(bc)+(ac)) \\ \end{gathered}[/tex]

so

Let

[tex]\begin{gathered} (a+b+c)=9 \\ ab+bc+ac=40 \\ \text{now, replace} \end{gathered}[/tex]

[tex]\begin{gathered} (a+b+c)^2=a^2+b^2+c^2+2((ab)+(bc)+(ac)) \\ 9^2=a^2+b^2+c^2+2(40) \\ 81=a^2+b^2+c^2+80 \\ \text{subtract 80 in both sides} \\ 81-80=a^2+b^2+c^2+80-80 \\ 1=a^2+b^2+c^2 \end{gathered}[/tex]

hence

[tex]a^2+b^2+c^2=1[/tex]

I hope this helps you

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