Question

A equação 2x²-7x+3=0 possui duas raízes reais .Sendo x, a maior delas e x² a menor, então , x¹,-x² é igual a:

Answer 1

Olá,

$ax^2\pm bx\pm c=0\\\\2x^2-7x+3=0\\\\Coeficientes:\;a=2,\;b=-7\;e\;c=3\\\\\Delta=b^2-4ac\\\Delta=(-7)^2-4\cdot2\cdot3\\\Delta=49-24\\\Delta=25\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\x=\dfrac{-(-7)\pm\sqrt{25}}{2\cdot2}\\\\x=\dfrac{7\pm5}{4}\\\\x_1=\dfrac{7+5}{4}=\dfrac{12}{4}=3\\\\x_2=\dfrac{7-5}{4}=\dfrac{2}{4}=0,5\\\\\boxed{x_1-x_2=3-0,5=2,5}$

Answer 2

Resposta:

x¹ - x²= 5/2

Explicação passo-a-passo:

2x² -7x +3 =0

a= 2     b= -7     c= 3

aplicando Baskara temos:

x= -b+- Vb²-4ac/2a

x=7+- V49-4*2*3 /2*2

x= 7+- V49-24 /4

x= 7+-V25 /4

x= 7+-5 /4

x¹= (7+5)/4

x¹= 12/4

x¹=3

x²= (7-5)/4

x² =2/4

x²= 1/2

então a diferença :

x¹ - x²= 3 - 1/2 = 6/2 -1/2 = 5/2