if a, b, c are all different and 1+a21+b21+c2abca3b3c3=0 then a+b+c=

1+a21+b21+c2abca3b3c3=0111abca3b3c3+a2b2c2abca3b3c3=0(a+b+c) (a-b0 (b-c) (c-a)+-(a-b) (b-c) (c-a)abc=0(a-b) (b-c) (c-a) (a+b+c)-abc=0but a, b, c are all different, then a+b+c-abc=0∴ a+b+c=abc

if a, b, c are all different and 1+a21+b21+c2abca3b3c3=0 then a+b+c=

1+a21+b21+c2abca3b3c3=0111abca3b3c3+a2b2c2abca3b3c3=0(a+b+c) (a-b0 (b-c) (c-a)+-(a-b) (b-c) (c-a)abc=0(a-b) (b-c) (c-a) (a+b+c)-abc=0but a, b, c are all different, then a+b+c-abc=0∴ a+b+c=abc

AI Mentor

Check Your IQ

Free Expert Demo

Try Test

Courses

Dropper NEET Course Dropper JEE Course Class - 12 NEET Course Class - 12 JEE Course Class - 11 NEET Course Class - 11 JEE Course Class - 10 Foundation NEET Course Class - 10 Foundation JEE Course Class - 10 CBSE Course Class - 9 Foundation NEET Course Class - 9 Foundation JEE Course Class -9 CBSE Course Class - 8 CBSE Course Class - 7 CBSE Course Class - 6 CBSE Course

Offline Centres

if a, b, c are all different and $|\begin{matrix} 1 + a^{2} & 1 + b^{2} & 1 + c^{2} \\ a & b & c \\ a^{3} & b^{3} & c^{3} \end{matrix}| = 0$ then $a + b + c =$

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$abc$

$a + b + c$

$ab + bc + ca$

answer is A.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{rcl} |\begin{matrix} 1 + a^{2} & 1 + b^{2} & 1 + c^{2} \\ a & b & c \\ a^{3} & b^{3} & c^{3} \end{matrix}| & = & 0 \\ |\begin{matrix} 1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3} \end{matrix}| + |\begin{matrix} a^{2} & b^{2} & c^{2} \\ a & b & c \\ a^{3} & b^{3} & c^{3} \end{matrix}| & = & 0 \end{array}$

$\begin{array}{rcl} (a + b + c) (a - b 0 (b - c) (c - a) + [- (a - b) (b - c) (c - a) abc] & = & 0 \\ (a - b) (b - c) (c - a) [(a + b + c) - abc] & = & 0 \end{array}$