Explicație pas cu pas:
d1²+d2²-10d1-8d2+41=0 =>
d1²-10d1+25+d2²-8d2+16=0 =>
(d1-5)²+(d2-4)²=0 <=> d1-5=0 si d2-4=0 => d1=5 si d2=4
A=d1*d2/2=20/2=10cm²
d1²+d2²-18d1-4d2+85=0 =>
d1²-18d1+81+d2²-4d2+4=0 =>
(d1-9)²+(d2-2)²=0 => d1-9=0=>d1=9cm si d2-2=0 =>d2=2
=> A=d1*d2/2=18/2=9cm²
4x²+y²+4=4(y+2V5x-5)=>
4x²+y²+4=4y+8V5x-20=>
4x²+y²+4-4y-8V5x+20=0 =>
4x²-8V5x+20+y²-4y+4=0=>
(2x-2V5)²+(y-2)²=0 <=> 2x-2V5=0 => 2x=2V5=> x=2
y-2=0 => y=2 => x=y
x(x+2V3)+y(y+2V2)=-5 =>
x²+2xV3+y²+2V2y+5=0 =>
x²+2xV3+3+y²+2V2y+2=0 =>
(x+V3)²+(y+V2)²=0 <=> x+V3=0 => x=-V3
y+V2=0 => y=-V2 => y>x
