Question

Calcule x e y:
A)x + 4 + ✓2y +2 = 6x + 8 + ✓y-4

B) x + 2 + ✓5y + 2 = 2x + 14 + ✓y-3

Answer 1

Efetuando os semelhantes encontramos para x e y os seguintes resultados

A)x + 4 + ✓2y +2 = 6x + 8 + ✓y-4

$x + 4 + \sqrt{2y} +2 = 6x + 8 + \sqrt{y-4} \\x + \sqrt{2y} +6 = 6x + 8 + \sqrt{y-4}\\\sqrt{2y}= 6x-x+ 8-6 + \sqrt{y-4}\\\sqrt{2y}= 5x+ 2 + \sqrt{y-4}$

 $(\sqrt{2y})^{2} =( 5x+ 2 + \sqrt{y-4})^{2} \\2y= 25x^{2}  + 4 + y - 4\\ 2y= 25x^{2}   + y \\ y= 25x^{2}$

B) x + 2 + ✓5y + 2 = 2x + 14 + ✓y-3

$x+2+\sqrt{5y}+2=2x+14+\sqrt{y-3} \\\sqrt{5y}=x+10+\sqrt{y-3} \\\sqrt{5y}^{2}=(x+10+\sqrt{y-3})^{2} \\5y=x^{2} +100+y-3 \\4y=x^{2} + 97$