If a - b - c - 0- the value of a2bc - b2ca - c2ab is abc - 0

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Byju's Answer

Standard XII

Mathematics

Sequence

If a + b + ...

Question

If $a + b + c = 0$ , the value of $\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b}$ is $(a b c \neq 0)$

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Solution

The correct option is D $3$
Since $a + b + c = 0$
or $a + b = - c$
or $(a + b)^{3} = - c^{3}$
or $a^{3} + b^{3} + 3 a b (a + b) = - c^{3}$
or $a^{3} + b^{3} + 3 a b (- c) = - c^{3}$
or $a^{3} + b^{3} + c^{3} = 3 a b c$
Dividing both the sides by $a b c$ , we get
$\frac{a^{2}}{b c} + \frac{b^{2}}{a c} + \frac{c^{2}}{a b} = 3$

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Similar questions

If $a b + b c + c a = 0$ , then the value of $\frac{1}{a^{2} - b c} + \frac{1}{b^{2} - c a} + \frac{1}{c^{2} - a b}$ will be:

A. $- 1$
B. $a + b + c$
C. $a b c$
D. $0$

If a + b + c = 0, then write the value of $\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b} .$

Q. If a+b+c=0 what is the value of

\frac{a^{2} + b^{2} + a b}{b^{2} + c^{2} + b c} + \frac{c^{2} + c a + a^{2}}{b^{2} + c^{2} + b c}

If a+b+c=0 then $(\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b})$ =?
(a) 1 (b) 0 (c) -1 (d) 3

Q. If a+b+c=0, The value of

\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b}

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If a+b+c=0, the value of a2bc+b2ca+c2ab is (abc≠0)

The correct option is D 3Since a+b+c=0or a+b=−cor (a+b)3=−c3or a3+b3+3ab(a+b)=−c3or a3+b3+3ab(−c)=−c3or a3+b3+c3=3abcDividing both the sides by abc, we geta2bc+b2ac+c2ab=3

If $a + b + c = 0$ , the value of $\frac{a^{2}}{b c} + \frac{b^{2}}{c a} + \frac{c^{2}}{a b}$ is $(a b c \neq 0)$