Solve:? 5x (1 + 1/(x^2 + y^2)) = 125x(1+1x2+y2)=12 and 5y (1 - 1/(x^2 + y^2)) = 45y(1−1x2+y2)=4

2 Answers
Sunayan S
Jan 16, 2018

See the answer below...

Explanation:

5x(1+1/(x^2+y^2))=125x(1+1x2+y2)=12color(red)" | " | 5y(1-1/(x^2+y^2))=45y(1−1x2+y2)=4
=>(1+1/(x^2+y^2))=12/(5x)⇒(1+1x2+y2)=125xcolor(red)" |" |=>(1-1/(x^2+y^2))=4/(5y)⇒(1−1x2+y2)=45y

From both equation,

color(red)(12/(5x)+4/(5y)=2125x+45y=2
=>12/(5x)=2-4/(5y)⇒125x=2−45y
=>6/(5x)=1-2/(5y)⇒65x=1−25y
=>(5x)/6=(5y)/(5y-2)⇒5x6=5y5y−2
=>x=(6y)/(5y-2)⇒x=6y5y−2

Putting it in first equation,
color(green)(5cdot(6y)/(5y-2){1+1/(y^2+((6y)/(5y-2))^2)}=125⋅6y5y−2⎧⎪ ⎪⎨⎪ ⎪⎩1+1y2+(6y5y−2)2⎫⎪ ⎪⎬⎪ ⎪⎭=12

Help me now.

Cesareo R.
Jan 16, 2018

See below.

Explanation:

x^2+y^2 = (5x)/(12-5x)x2+y2=5x12−5x
x^2+y^2=(5y)/(4-5y)x2+y2=5y4−5y

now

(5x)/(12-5x) = (5y)/(4-5y) rArr x = 3y5x12−5x=5y4−5y⇒x=3y then

(3y)^2+y^2 = (5y)/(4-5y) rArr 10y = 5/(4-5y)(3y)2+y2=5y4−5y⇒10y=54−5y

y = {(1/10(4-sqrt6)),(1/10(4+sqrt6)):}

x = {(1/30(4-sqrt6)),(1/30(4+sqrt6)):}

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