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If the line y=root 3x interests the curve x^3+y^3+3xy+5x^2+3y^2+4x+5y1=0 At 3 points A,B,C .Then find OA*OB*OC...
 one year ago
 one year ago
PLEASE HELP!! If the line y=root 3x interests the curve x^3+y^3+3xy+5x^2+3y^2+4x+5y1=0 At 3 points A,B,C .Then find OA*OB*OC...
 one year ago
 one year ago

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DLSBest ResponseYou've already chosen the best response.0
dw:1353211730667:dw SMT lyk this?
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.0
Is it dw:1353224657415:dw
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.0
Is it dw:1353225679747:dw
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.0
y=root 3x ..............i x^3+y^3+3xy+5x^2+3y^2+4x+5y1=0 ............ii Now, From i and ii, (1+3root3)x^3 + (14+3root3)x^2 + (4+5root3)x1=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)
 one year ago

DLSBest ResponseYou've already chosen the best response.0
\[x^3+y^3+3xy+5x^2+3y^2+4x+5y1=0\] is the equation :(
 one year ago

DLSBest ResponseYou've already chosen the best response.0
\[y=\sqrt{3}x\] is the line
 one year ago

sauravshakyaBest ResponseYou've already chosen the best response.0
oh yes it is 8/(3root3 +1) y=root 3x ..............i x^3+y^3+3xy+5x^2+3y^2+4x+5y1=0 ............ii Now, From i and ii, (1+3root3)x^3 + (14+3root3)x^2 + (4+5root3)x1=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)
 one year ago
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