﻿ The line x + y = 1 meets the line represented by the equation y3 –xy2 – 14x2y + 24x3 = 0 at the points A, B, C. If O is the origin, then OA2 + OB2 + OC2 is equal to     : Kaysons Education

# The Line x + y = 1 Meets The Line Represented By The Equation y3 –xy2 – 14x2y + 24x3 = 0 At The Points A, B, C. If O is The Origin, Then OA2 + OB2 + OC2 is Equal To

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## Question

### Solution

Correct option is

221/72

x-coordinates of the points are given by

24x3 + 14x2 (x – 1) – x (x – 1)2 – (x – 1)3 = 0

⇒ 36x3 – 9x2 – 4x + 1 = 0

⇒ (3x – 1) (3x + 1) (4x – 1) = 0

⇒ x = 1/3, –1/3, 1/4

⇒ A (1/3, 2/3), B (–1/3, 4/3) and C (1/4, 3/4)

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