## DLS 2 years ago PLEASE HELP!! If the line y=root 3x interests the curve x^3+y^3+3xy+5x^2+3y^2+4x+5y-1=0 At 3 points A,B,C .Then find OA*OB*OC...

1. DLS

|dw:1353211730667:dw| SMT lyk this?

2. DLS

@sauravshakya

3. sauravshakya

Is O the origin?

4. DLS

yes

5. sauravshakya

Is it |dw:1353224657415:dw|

6. DLS

yes

7. sauravshakya

Is it |dw:1353225679747:dw|

8. sauravshakya

@DLS

9. DLS

whatts that:o

10. sauravshakya

y=root 3x ..............i x^3+y^3+3xy+5x^2+3y^2+4x+5y-1=0 ............ii Now, From i and ii, (1+3root3)x^3 + (14+3root3)x^2 + (4+5root3)x-1=0 x^3 + (14+3root3)/(1+3root3)x^2 + (4+5root3)/(1+3root3)x -1/(1 + 3root3) =0 Now product of all the roots of this cubic equation is -1/(1+3root3) Now, OA*OB*OC = 8*3root3*product of all the roots of the above cubic equation =-24root3 /(1+3root3)

11. DLS

its 8/3root3 +1

12. DLS

$x^3+y^3+3xy+5x^2+3y^2+4x+5y-1=0$ is the equation :(

13. DLS

$y=\sqrt{3}x$ is the line

14. sauravshakya

oh yes it is 8/(3root3 +1) y=root 3x ..............i x^3+y^3+3xy+5x^2+3y^2+4x+5y-1=0 ............ii Now, From i and ii, (1+3root3)x^3 + (14+3root3)x^2 + (4+5root3)x-1=0 x^3 + (14+3root3)/(1+3root3)x^2 + (4+5root3)/(1+3root3)x -1/(1 + 3root3) =0 Now product of all the roots of this cubic equation is -{-1/(1+3root3)} NOTE: it is -ve since it is a cubic equation which has odd number of roots Now, OA*OB*OC = 8*product of all the roots of the above cubic equation =8/(1+3root3)

15. DLS

explain properly? ://