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daniil080401q
@daniil080401q
August 2022
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x^2+y^2=100 | xy=48
СИСТЕМУ РЕШИТЬ ПЛИИМИИЗ
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oganesbagoyan
Verified answer
{(x+y)² -2xy =100 ; xy =48 .⇔{(x+y)² -2xy =100 ; xy =48 .
{(x+y)² =14² ; xy =48 .
{ x+y = ± 14 ; xy =48 .
a) { x+y = - 14 ; xy =48 .⇒
( -6 ; -8) ;(-8 ;-6).
б){ { x+y = 14 ; xy =48 .⇒
(6 ;8) ,(8;6) .
* * * * * * * * * * * * * * *
{ x+y = - 14 ; xy =48 ;
{ y = - 14 -x ; x( -14 -x) =48 ;
x( -14 -x) =48 ;
x ² +14x +48 = 0;
x = -7±√(7² -48) ;
x₁ = -7 -1 = -8 ⇒y₁ = -14 -x₁ = -14 -(-8) = - 6.
x₂ = -7 +1 =8 ⇒ y₂ = -14 -x₂ = -14 -(-6) = - 8.
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daniil080401q
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Answers & Comments
Verified answer
{(x+y)² -2xy =100 ; xy =48 .⇔{(x+y)² -2xy =100 ; xy =48 .{(x+y)² =14² ; xy =48 .
{ x+y = ± 14 ; xy =48 .
a) { x+y = - 14 ; xy =48 .⇒ ( -6 ; -8) ;(-8 ;-6).
б){ { x+y = 14 ; xy =48 .⇒(6 ;8) ,(8;6) .
* * * * * * * * * * * * * * *
{ x+y = - 14 ; xy =48 ;
{ y = - 14 -x ; x( -14 -x) =48 ;
x( -14 -x) =48 ;
x ² +14x +48 = 0;
x = -7±√(7² -48) ;
x₁ = -7 -1 = -8 ⇒y₁ = -14 -x₁ = -14 -(-8) = - 6.
x₂ = -7 +1 =8 ⇒ y₂ = -14 -x₂ = -14 -(-6) = - 8.