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let-x-and-y-such-that-2x-2-4x-2y-0-y-2-x-6-2-0-find-the-possibles-value-of-x-y-

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Question Number 34211 by candre last updated on 02/May/18
let x and y such that 2x^2 +4x−2y=0 y^2 −(x+6)^2 =0 find the possibles value of x+y
letxandysuchthat2x2+4x−2y=0y2−(x+6)2=0findthepossiblesvalueofx+y
Answered by MJS last updated on 02/May/18
I. 2x^2 +4x−2y=0 II. y^2 −(x+6)^2 =0 ⇒ y=±(x+6) case 1 y=−x−6 ⇒ x+y=−6 2x^2 +4x−2(−x−6)=0 2x^2 +6x+12=0 x_1 =−(3/2)−((√7)/2)i; y_1 =−(9/2)+((√7)/2)i x_2 =−(3/2)+((√7)/2)i; y_2 =−(9/2)−((√7)/2)i case 2 y=x+6 2x^2 +4x−2(x+6)=0 2x^2 +2x−12=0 x_3 =−3; y_3 =3 x_4 =2; y_4 =8 x, y∈C ⇒ (x+y)∈{−6; 0; 10} x, y∈R ⇒ (x+y)∈{0; 10}
I.2x2+4x−2y=0II.y2−(x+6)2=0⇒y=±(x+6)case1y=−x−6⇒x+y=−62x2+4x−2(−x−6)=02x2+6x+12=0x1=−32−72i;y1=−92+72ix2=−32+72i;y2=−92−72icase2y=x+62x2+4x−2(x+6)=02x2+2x−12=0x3=−3;y3=3x4=2;y4=8x,y∈C⇒(x+y)∈{−6;0;10}x,y∈R⇒(x+y)∈{0;10}

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