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y=4.905*((2-y)/(331))^2

Solución

y = 4.905 \cdot (\frac{2 - y}{331})^{2}

y = \frac{21916124 + 981 \frac{2191612 4 ^{2}}{962361} - 16}{1962}, y = \frac{21916124 - 981 \frac{2191612 4 ^{2}}{962361} - 16}{1962}

Notación decimal

y = 22340.59513 \dots, y = 0.00017 \dots

Pasos de solución

y = 4.905 (\frac{2 - y}{331})^{2}

Multiplicar ambos lados por

1000

y \cdot 1000 = \frac{4905 ( 2 - y ) ^{2}}{109561}

Multiplicar ambos lados por

109561

109561000 y = 4905 (2 - y)^{2}

Desarrollar

4905 (2 - y)^{2} : 19620 - 19620 y + 4905 y^{2}

109561000 y = 19620 - 19620 y + 4905 y^{2}

Intercambiar lados

19620 - 19620 y + 4905 y^{2} = 109561000 y

Mover

109561000 y

al lado izquierdo

4905 y^{2} - 109580620 y + 19620 = 0

Dividir ambos lados entre

4905

\frac{4905 y ^{2}}{4905} - \frac{109580620 y}{4905} + \frac{19620}{4905} = \frac{0}{4905}

Escribir en la forma binómica

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

y^{2} - \frac{21916124 y}{981} + 4 = 0

Resolver con la fórmula general para ecuaciones de segundo grado:

y_{1, 2} = \frac{- ( - \frac{21916124}{981} ) \pm ( - \frac{21916124}{981} ) ^{2} - 4 \cdot 1 \cdot 4}{2 \cdot 1}

(- \frac{21916124}{981})^{2} - 4 \cdot 1 \cdot 4 = \frac{2191612 4 ^{2}}{962361} - 16

y_{1, 2} = \frac{- ( - \frac{21916124}{981} ) \pm \frac{2191612 4 ^{2}}{962361} - 16}{2 \cdot 1}

Separar las soluciones

y_{1} = \frac{- ( - \frac{21916124}{981} ) + \frac{2191612 4 ^{2}}{962361} - 16}{2 \cdot 1}, y_{2} = \frac{- ( - \frac{21916124}{981} ) - \frac{2191612 4 ^{2}}{962361} - 16}{2 \cdot 1}

y = \frac{- ( - \frac{21916124}{981} ) + \frac{2191612 4 ^{2}}{962361} - 16}{2 \cdot 1} : \frac{21916124 + 981 \frac{2191612 4 ^{2}}{962361} - 16}{1962}

y = \frac{- ( - \frac{21916124}{981} ) - \frac{2191612 4 ^{2}}{962361} - 16}{2 \cdot 1} : \frac{21916124 - 981 \frac{2191612 4 ^{2}}{962361} - 16}{1962}

Las soluciones a la ecuación de segundo grado son:

y = \frac{21916124 + 981 \frac{2191612 4 ^{2}}{962361} - 16}{1962}, y = \frac{21916124 - 981 \frac{2191612 4 ^{2}}{962361} - 16}{1962}

- 575 - 3

- 16 x^{2} + 16 x + 480 = 0

- \frac{2 x + 3}{( x - 1 ) ^{2} ( x + 4 ) ^{2}} < 0

0 = (x + 4)^{2} - 2

19 \leq 5 x - 1 \leq 39