European School Test - Can you solve this for x,y?

[@Marinealver]

Finally, a nice little problem without complex solutions.

[@ampleyfly]

You can make the observations that: since x + y = 5 but x * y = 25, x and y must be complex, but since their sum and products are real they must be conjugates. This makes Re(x) = Re(y) = 5/2, Im(x) = - Im(y), and |x|^2 = 25 => Im(x) = +- sqrt(75)/2.

[@marilynman]

An alternative is just multiplying the first equation by x -> x^2+xy=5x and substitute xy, which I think it's easier for problems that have nonlinear relationships like the problem ab=100, bc=200, ac=300 or some derivation of it.

[@prostoneznaju]

Could you make it shorter? Some repetitions are redundant.

[@ApexGC91732]

thats the easiest question I ever seen x+y=5 xy=25 first half of 5 Is 2.5 =(2.5-c)+(2.5+c)=5 (2.5-c)(2.5+c)=25 (2.5)²-C²=25 6.25-25=C² C²=-18.75 C=√-18.75 now x= 2.5-i√18.75 y=2.5+i√18.75

[@RealQinnMalloryu4]

(2)+(3)=5 (y ➖ 3x+2).(xy ➖ 5xy+5).

[@32shouryajadounvi-e50]

NGL this was easier than I thought

[@БогданиРадмирИльгизовы]

You said that you could show us another solution, when are you going to show it?

[@БогданиРадмирИльгизовы]

Fourth?

[@veli-pl9bx]

I solved it and it became true🗿

[@QT-8]

Third

[@NounPhechnai]

Second

[@furkansamed9231]

fourth

[@SerigalaNews]

First

[@elenagavrilova3109]

приведите ногти в порядок, пожалуйста.

[@БогданиРадмирИльгизовы]

😂 вы не математикой занимались, не так ли?😅