Question

Ajutati-ma va rog cu ecuatia:

x²-3x√(2x-1)+2(2x-1)=0

Answer 1

[tex] x^{2} -3x \sqrt{2x-1} +2(2x-1)=0 [/tex]
$x^{2} -x \sqrt{2x-1}-2x \sqrt{2x-1} +2(2x-1)=0$$x(x -\sqrt{2x-1})-2\sqrt{2x-1}(x -\sqrt{2x-1})=0$$(x -\sqrt{2x-1})(x-2\sqrt{2x-1})=0$$[tex](x =\sqrt{2x-1}) ; x^{2} =2x-1; x^{2} -2x+1=0; (x-1)^{2} =0; x1=1$;
 
$x-2\sqrt{2x-1}=0; x=2\sqrt{2x-1}; x^{2} =4(2x-1); x^{2} -8x+4)=0$
Δ=64-16=48
x2=4+2√3
x3=4-2√3 Nu este solutie- din conditiile de existenta ale radicalilor