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(5.97210^{24})(3.8310^5-x)^2=x^2(7.3510^{22})

Solution

(5.972 \cdot 1 0^{24}) (3.83 \cdot 1 0^{5} - x)^{2} = x^{2} \cdot (7.35 \cdot 1 0^{22})

x = \frac{775544.96905 \dots + 775544.96905 \dots ^{2} - 594067446299.9067}{2}, x = \frac{775544.96905 \dots - 775544.96905 \dots ^{2} - 594067446299.9067}{2}

Décimale

x = 430791.52895 \dots, x = 344753.44010 \dots

étapes des solutions

(5.972 \cdot 1 0^{24}) (3.83 \cdot 1 0^{5} - x)^{2} = x^{2} (7.35 \cdot 1 0^{22})

Développer

(5.972 \cdot 1 0^{24}) (3.83 \cdot 1 0^{5} - x)^{2} : 1 0^{34} \cdot 3.8 3^{2} \cdot 5.972 - 1 0^{29} \cdot 45.74552 x + 1 0^{24} \cdot 5.972 x^{2}

1 0^{34} \cdot 3.8 3^{2} \cdot 5.972 - 1 0^{29} \cdot 45.74552 x + 1 0^{24} \cdot 5.972 x^{2} = x^{2} (7.35 \cdot 1 0^{22})

Déplacer

x^{2} \cdot (7.35 \cdot 1 0^{22})

vers la gauche

1 0^{34} \cdot 3.8 3^{2} \cdot 5.972 - 1 0^{29} \cdot 45.74552 x + 1 0^{22} x^{2} (1 0^{2} \cdot 5.972 - 7.35) = 0

Diviser les deux côtés par

1 0^{22} \cdot 589.85

\frac{1 0 ^{34} \cdot 3.8 3 ^{2} \cdot 5.972}{1 0 ^{22} \cdot 589.85} - \frac{1 0 ^{29} \cdot 45.74552 x}{1 0 ^{22} \cdot 589.85} + \frac{1 0 ^{22} x ^{2} ( 1 0 ^{2} \cdot 5.972 - 7.35 )}{1 0 ^{22} \cdot 589.85} = \frac{0}{1 0 ^{22} \cdot 589.85}

Ecrire sous la forme standard

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

x^{2} - 775544.96905 \dots x + 148516861574.97668 = 0

Résoudre par la formule quadratique

x_{1, 2} = \frac{- ( - 775544.96905 \dots ) \pm ( - 775544.96905 \dots ) ^{2} - 4 \cdot 1 \cdot 148516861574.97668}{2 \cdot 1}

(- 775544.96905 \dots)^{2} - 4 \cdot 1 \cdot 148516861574.97668 = 775544.96905 \dots^{2} - 594067446299.9067

x_{1, 2} = \frac{- ( - 775544.96905 \dots ) \pm 775544.96905 \dots ^{2} - 594067446299.9067}{2 \cdot 1}

Séparer les solutions

x_{1} = \frac{- ( - 775544.96905 \dots ) + 775544.96905 \dots ^{2} - 594067446299.9067}{2 \cdot 1}, x_{2} = \frac{- ( - 775544.96905 \dots ) - 775544.96905 \dots ^{2} - 594067446299.9067}{2 \cdot 1}

x = \frac{- ( - 775544.96905 \dots ) + 775544.96905 \dots ^{2} - 594067446299.9067}{2 \cdot 1} : \frac{775544.96905 \dots + 775544.96905 \dots ^{2} - 594067446299.9067}{2}

x = \frac{- ( - 775544.96905 \dots ) - 775544.96905 \dots ^{2} - 594067446299.9067}{2 \cdot 1} : \frac{775544.96905 \dots - 775544.96905 \dots ^{2} - 594067446299.9067}{2}

Les solutions de l'équation de forme quadratique sont :

x = \frac{775544.96905 \dots + 775544.96905 \dots ^{2} - 594067446299.9067}{2}, x = \frac{775544.96905 \dots - 775544.96905 \dots ^{2} - 594067446299.9067}{2}

s im pl i f y \frac{1}{2} x^{- 2}

3 x^{2} - 12 x = 9

- 3 c + 15 = 3

s im pl i f y \frac{( a + b ) ^{9}}{( a + b ) ^{4}}

\frac{x}{2} \leq \frac{5}{8}