Hi Everbody, I am a new member to this forum.I am from INDIA and studying in grade 12. I was struck in a question and need help.Hope someone could solve it. The question is to solve these simultaneous equations:- √x + y = a -------- (i) x +√y = b ---------- (ii) I have a few hints such as making a change in variable by introducing x = m^2 and y= n^2 and then doing some algebraic manipulations to get (m-n)(1-m-n)=a-b But I dunno know what to do next. Plz help.
Those "algebraic manipulations" don't help because you are left with one equation in two variables. After you have m^{2}+ n= b and m+ n^{2}= a, you can solve the first for n: n= b- m^{2} and then substitute in the second: m+ (b-m^{2})^{2}= a. That gives a single, fourth degree, equation for m.
sqrt(x)+y=a Sqrt(y)+x=b I'd simply...use a substitution after working around w/ them sqrt(x)=a-y sqrt(y)=b-x x=a^2 - 2ay + y^2 y=b^2 -2bx + x^2 And now...stick the x into the y= y=B^2 -2b(a^2 - 2ay + y^2) + (a^2 - 2ay + y^2)^2 And algebrate. it's ugly but you can't dodge the forth power I don't think. SUbstitute y from both sides and you'll have the =0