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If p + q + r = 1 and a + b + c = 0 a b c p q r where p, q, r and a, b, c are non-zero, then the value of p2 + q2 + r2 is a2 b2 c2
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Correct Option: C
| Let | = x , | = y , | = z | |||
| a | b | c |
∴ x + y + z = 1
| and | + | + | = 0 | |||
| x | y | z |
| ⇒ | = 0 | |
| xyz |
⇒ yz + xz + xy = 0
∴ x + y + z = 1
On squaring both sides ,
x2 + y2 + z2 + 2xy + 2yz + 2zx = 1
⇒ x2 + y2 + z2 + 0 = 1
⇒ x2 + y2 + z2 = 1
