solvefor x,2^2=h(x)^2+(x/2)^2

Solución

resolver para

x, 2^{2} = h (x)^{2} + (\frac{x}{2})^{2}

x = \frac{4}{4 h + 1}, x = - \frac{4}{4 h + 1}; h \neq = - \frac{1}{4}

Pasos de solución

2^{2} = h x^{2} + (\frac{x}{2})^{2}

Desarrollar

2^{2} : 4

Desarrollar

h x^{2} + (\frac{x}{2})^{2} : x^{2} h + \frac{x ^{2}}{4}

4 = x^{2} h + \frac{x ^{2}}{4}

Intercambiar lados

x^{2} h + \frac{x ^{2}}{4} = 4

Mover

4

al lado izquierdo

x^{2} h + \frac{x ^{2}}{4} - 4 = 0

Escribir en la forma binómica

a x^{2} + b x + c = 0

(h + \frac{1}{4}) x^{2} - 4 = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

x_{1, 2} = \frac{- 0 \pm 0 ^{2} - 4 ( h + \frac{1}{4} ) ( - 4 )}{2 ( h + \frac{1}{4} )}

Simplificar

0^{2} - 4 (h + \frac{1}{4}) (- 4) : 2 4 h + 1

x_{1, 2} = \frac{- 0 \pm 2 4 h + 1}{2 ( h + \frac{1}{4} )}; h \neq = - \frac{1}{4}

Separar las soluciones

x_{1} = \frac{- 0 + 2 4 h + 1}{2 ( h + \frac{1}{4} )}, x_{2} = \frac{- 0 - 2 4 h + 1}{2 ( h + \frac{1}{4} )}

x = \frac{- 0 + 2 4 h + 1}{2 ( h + \frac{1}{4} )} : \frac{4}{4 h + 1}

x = \frac{- 0 - 2 4 h + 1}{2 ( h + \frac{1}{4} )} : - \frac{4}{4 h + 1}

Las soluciones a la ecuación de segundo grado son:

x = \frac{4}{4 h + 1}, x = - \frac{4}{4 h + 1}; h \neq = - \frac{1}{4}

4 x^{2} + y^{2} \leq 17

0.5 = 4 x^{2} + y^{2}

\frac{x ^{2}}{9} + y^{2} > 9

\frac{( x + 8 ) ^{2}}{20} + \frac{( y + 36 ) ^{2}}{36} = 1

4 x^{2} + y^{2} - 16 x - 2 y + 1 = 0