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Question Number 111497 by bemath last updated on 04/Sep/20

Commented by kaivan.ahmadi last updated on 04/Sep/20

let t=x_1 ^3 +6x_1 ^2 −30x_1 +x_1 ^2 x_2 −5x_1 ^2 x^2 +6x+7=0 x_1 ^2 +6x_1 =−7 and x^3 +6x^2 +7x=0⇒x_1 ^3 +6x_1 ^2 =−7x_1 ⇒x_1 ^3 +6x_1 ^2 −30x_1 =−7x_1 −30x_1 =−37x_1 ⇒t=−37x_1 +x_1 ^2 x_2 −5x_1 ^2 =x_1 (−37+x_1 x_2 )−5x_1 ^2 = x_1 (−37+7)−5x_1 ^2 =−30x_1 −5x_1 ^2 =−5(x_1 ^2 +6x_1 ) =−5×(−7)=35

lett=x13+6x12−30x1+x12x2−5x12x2+6x+7=0x12+6x1=−7andx3+6x2+7x=0⇒x13+6x12=−7x1⇒x13+6x12−30x1=−7x1−30x1=−37x1⇒t=−37x1+x12x2−5x12=x1(−37+x1x2)−5x12=x1(−37+7)−5x12=−30x1−5x12=−5(x12+6x1)=−5×(−7)=35

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