ICSE BoardEnglish MediumSTD 9MATHEMATICSExpansions (Including Substitution)2 Marks
Question
If $a + b + c = p$ and $ab + bc + ca = q ;$ find $a^2+ b^2+ c^2.$
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Answer
We know that
$( a + b + c )^2 = a^2 + b^2 + c^2 + 2( ab + bc + ca ) .....(1)$
Given that, $a + b + c = p$ and $ab + bc + ca = q$
We need to find $a^2 + b^2 + c^2 :$
Substitute the values of $( ab + bc + ca )$ and $( a + b + c )$
in the identity $(1),$ we have
$(p)^2 = a^2 + b^2 + c^2 + 2q$
$\Rightarrow p^2 = a^2 + b^2 + c^2 + 2q$
$\Rightarrow a^2 + b^2 + c^2$
$= p^2 - 2q$
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