Question

como fatorar a raiz quadrada de 40?​

Answer 1

Resposta:

40 | 2

20 | 2

10 | 2

5 | 5

1 | 1  = 2 . 2 . 2 . 5 = 2².2.5=2².10=40

√40=√(2².10)=√2².√10=2√10

-x-x-x-x-x-x-x

2x²-5=0

2x²=5

x²=5/2

x=±√(5/2)=±√5/√2=±√5/√2*(√2/√2)=±(√5*√2)/2=±√10/2

ou

$Aplicando~a~f\'{o}rmula~de~Bhaskara~para~2x^{2}-0x-5=0~~\\e~comparando~com~(a)x^{2}+(b)x+(c)=0,~temos~a=2{;}~b=0~e~c=-5\\\\\Delta=(b)^{2}-4(a)(c)=(0)^{2}-4(2)(-5)=0-(-40)=40\\\\x^{'}=\frac{-(b)-\sqrt{\Delta}}{2(a)}=\frac{-(0)-\sqrt{40}}{2(2)}=\frac{0-2\sqrt{10}}{4}=-\frac{\sqrt{10}}{2}\\\\x^{''}=\frac{-(b)+\sqrt{\Delta}}{2(a)}=\frac{-(0)+\sqrt{40}}{2(2)}=\frac{0+2\sqrt{10}}{4}=\frac{\sqrt{10}}{2}\\\\S=\{-\frac{\sqrt{10}}{2},~\frac{\sqrt{10}}{2}}\}$