Question

If the point $\left( \frac { a ^ { 3 } } { a - 1 } , \frac { a ^ { 2 } - 3 } { a - 1 } \right)$, and

$\left( \frac { c ^ { 3 } } { c - 1 } , \frac { c ^ { 2 } - 3 } { c - 1 } \right)$ are collinear for distinct

a, b, c and aabc + b (a + b + c) + g (ab + bc + ca) = 0 then value of a² + b² + g² is-

• A. 10
• B. 9
• C. 4
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

Let the given point on the line lx + my + n = 0 then l $\left( \frac { x ^ { 3 } } { x - 1 } \right)$ + m$\left( \frac { x ^ { 2 } - 3 } { x - 1 } \right)$ + n = 0

Where x = a, b, c are roots of equation.

lx³ + mx² + nx – 3m – n = 0

Ž a + b + c = $- \frac { m } { \ell }$ , ab + bc + ca = $\frac { \mathrm { n } } { \ell }$ abc =

Ž abc – (ab + bc + ca) + 3 (a + b + c)

Ž – $\frac { \mathrm { n } } { \ell }$ – $\frac { 3 \mathrm {~m} } { \ell }$ = 0

Ž a = 1, b = 3, g = –1

Then a² + b² + g² = 1 + 9 + 1 = 11.