Question

Resolva a equação irracional.

Answer 1

$\sqrt{x+10} - \sqrt{2x-5} =0\\\\\\ ( \sqrt{x+10} - \sqrt{2x-5} )^2=(0)^2\to \\\\ x+10-2( \sqrt{x+10} )*( \sqrt{2x-5} )+2x-5=0\to \\\\ \sqrt{(x+10)*(2x-5)} = (\frac{3x+5}{2} )\to \\\\ ( \sqrt{(x+10)*(2x-5)} )^2= (\frac{3x+5}{2} )^2\to \\\\ 2 x^{2} -5x+20x-50= \frac{9 x^{2} +30x+25}{4} \to \\\\ 8 x^{2} +60x-200=9 x^{2} +30x+25\to \\\\ x^{2} -30x+225=0$


$a=1;b=-30;c=225\\\\ \Delta=b^2-4ac\to \Delta=(-30)^2-4*1*225\to \Delta=900-900\to \Delta=0\\\\ x= \frac{-b\pm \sqrt{\Delta} }{2a} \to x= \frac{-(-30)\pm \sqrt{0} }{2*1} \to x= \frac{30\pm 0 }{2} \to \\\\ x'=x''= \frac{30}{2} \to x'=x''=15$




$Verificando\to \\\\ \sqrt{x+10} - \sqrt{2x-5} =0\\\\ \sqrt{15+10} - \sqrt{2*15-5} =0\\\\ \sqrt{25} - \sqrt{30-5} =0\\\\ \sqrt{25} - \sqrt{25} =0\\\\ 5-5=0\\\\ 0=0$



Espero ter ajudado...