if a+b+c = 0 then the value of a^2/bc + b^2ca + c^2/ab = ?
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Answer:
Answer:
Value of \frac{a^{2}}{bc}+\frac{b^{2}}{ca}+\frac{c^{2}}{ab}
bc
a
2
+
ca
b
2
+
ab
c
2
= 33
Explanation:
Given a+b+c=0 ----(1)
we know the algebraic identity:
Value of \frac{a^{2}}{bc}+\frac{b^{2}}{ca}+\frac{c^{2}}{ab}
bc
a
2
+
ca
b
2
+
ab
c
2
= \frac{a^{3}}{abc}+\frac{b^{3}}{abc}+\frac{c^{3}}{abc}
abc
a
3
+
abc
b
3
+
abc
c
3
= \frac{a^{3}+b^{3}+c^{3}}{abc}
abc
a
3
+b
3
+c
3
= \frac{(a+b+c)(a^{2}+b^{2}+c^{2}-ab-bc-ca)+3abc}{abc}
abc
(a+b+c)(a
2
+b
2
+c
2
−ab−bc−ca)+3abc
= \frac{0\times(a^{2}+b^{2}+c^{2}-ab-bc-ca)+3abc}{abc}
abc
0×(a
2
+b
2
+c
2
−ab−bc−ca)+3abc
/* from (1) */
= \frac{3abc}{abc}
abc
3abc
= 33
Therefore,
Value of \frac{a^{2}}{bc}+\frac{b^{2}}{ca}+\frac{c^{2}}{ab}
bc
a
2
+
ca
b
2
+
ab
c
2
= 33
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