Math, asked by abdulbasithpqrs, 19 days ago

if a+b+c=6,and ab+bc+ca= 11,find the value of a²+b²+c²​

Answers

Answered by tp2984511
4

Answer:

c=6,and ab+bc+ca= 11,find the value of a²+b²+c²

Answered by BrainlyZendhya
23

We know that, It is given that,

  • \sf{a\:+\:b\:+\:c\:=\:6}
  • \sf{ab\:+\:bc\:+\:ca\:=\:11}

We also know that,

\sf{a^2\:+\:b^2\:+\:c^2} can be written as \sf{(a\:+\:b\:+\:c)^2}

\sf\implies{a^2\:+\:b^2\:+\:c^2\:=\:(a\:+\:b\:+\:c)^2}

Using Formula,

{\boxed{\bullet\:{(a\:+\:b\:+\:c)^2\:=\:a^2\:+\:b^2\:+\:c^2\:+\:2(ab\:+\:bc\:+\:ca)}}}

Substituting values in Formula,

\sf\implies{(a\:+\:b\:+\:c)^2\:=\:a^2\:+\:b^2\:+\:c^2\:+\:2(ab\:+\:bc\:+\:ca)}

\sf\implies{(a^2\:+\:b^2\:c^2)\:=\:(a\:+\:b\:+\:c)^2\:-\:2(ab\:+\:bc\:+\:ca)}

\sf\implies{a^2\:+\:b^2\:+\:c^2\:=\:(6)^2\:-\:2(11)}

\sf\implies{a^2\:+\:b^2\:+\:c^2\:=\:36\:-\:22}

\sf\implies{a^2\:+\:b^2\:+\:c^2\:=\:14}

Hence, the value of a² + b² + c² = 14.

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