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Identities — MATHS STD 8 — Question

ICSE BoardEnglish MediumSTD 8MATHSIdentities4 Marks
Question
Find : $a + b + c,$ if $a^2 + b^2 + c^2 = 83$ and $ab + bc + ca = 71.$
✓

Answer

$ (a+b+c)^2=a^2+b^2+c^2+2 a b+2 b c+2 c a$
$ \Rightarrow(a+b+c)^2=82+2(a b+b c+c a)$
$ \Rightarrow(a+b+c)^2=83+2 \times 71$
$ \Rightarrow(a+b+c)^2=83+142$
$ \Rightarrow(a+b+c)^2=225$
$ \Rightarrow a+b+c=\sqrt{225}$
$ \Rightarrow a+b+c= \pm 15$

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