If the points $$Pi=ai3ai-1$$,$$ai2-3ai-1$$, i $$=$$ $$1$$, $$2$$, $$3$$, , are collinear and $$a1$$, $$a2$$ and $$a3$$ are distinct real numbers, then

Correct option is 3a1a2a3-∑a1a2+3∑a1=0

Questions

If the points $P_{i} = (\frac{a_{i}^{3}}{a_{i} - 1}, \frac{a_{i}^{2} - 3}{a_{i} - 1}), i = 1, 2, 3$ , , are collinear and a_1, a₂ and a₃ are distinct real numbers, then

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a1a2a3-∑a1a2-3∑a1=0

a1a2a3+∑a1a2-3∑a1=0

a1a2a3-∑a1a2+3∑a1=0

-a1a2a3+∑a1a2-3∑a1=0

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detailed solution

Correct option is C

Let the given points lie on the line lx + my + n = 0∴ai3a1-1+mai2-3ai-1+n=0⇒lai3+mai2+nai-3m-n=0∴∑a1=-ml,∑a1a2=nl and a1a2a3=3m+nl∴a1a2a3-∑a1a2+3∑a1=0

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If the points Pi=ai3ai-1,ai2-3ai-1, i = 1, 2, 3, , are collinear and a1, a2 and a3 are distinct real numbers, then

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If the points $P_{i} = (\frac{a_{i}^{3}}{a_{i} - 1}, \frac{a_{i}^{2} - 3}{a_{i} - 1}), i = 1, 2, 3$ , , are collinear and a_1, a₂ and a₃ are distinct real numbers, then