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العربية

solvefor x,(x^2)/(c^2)-(y^9)/(d^2)=pix

الحلّ

solve for

x, \frac{x ^{2}}{c ^{2}} - \frac{y ^{9}}{d ^{2}} = π x

x = \frac{c ( π c d + 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}, x = \frac{c ( π c d - 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}; d \neq = 0

خطوات الحلّ

\frac{x ^{2}}{c ^{2}} - \frac{y ^{9}}{d ^{2}} = π x

Find Least Common Multiplier of

c^{2}, d^{2} : c^{2} d^{2}

c^{2} d^{2} =

اضرب بالمضاعف المشترك الأصغر

\frac{x ^{2}}{c ^{2}} c^{2} d^{2} - \frac{y ^{9}}{d ^{2}} c^{2} d^{2} = π x c^{2} d^{2}; c^{2} d^{2} \neq = 0

بسّط

d^{2} x^{2} - c^{2} y^{9} = π c^{2} d^{2} x; c^{2} d^{2} \neq = 0

انقل

π c^{2} d^{2} x

إلى الجانب الأيسر

d^{2} x^{2} - c^{2} y^{9} - π c^{2} d^{2} x = 0; c^{2} d^{2} \neq = 0

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

اكتب بالصورة الاعتياديّة

d^{2} x^{2} - π c^{2} d^{2} x - c^{2} y^{9} = 0; c^{2} d^{2} \neq = 0

حلّ بالاستعانة بالصيغة التربيعيّة

x_{1, 2} = \frac{- ( - π c ^{2} d ^{2} ) \pm ( - π c ^{2} d ^{2} ) ^{2} - 4 d ^{2} ( - c ^{2} y ^{9} )}{2 d ^{2}}

(- π c^{2} d^{2})^{2} - 4 d^{2} (- c^{2} y^{9})

بسّط:

c d π^{2} c^{2} d^{2} + 4 y^{9}

x_{1, 2} = \frac{- ( - π c ^{2} d ^{2} ) \pm c d π ^{2} c ^{2} d ^{2} + 4 y ^{9}}{2 d ^{2}}; d \neq = 0

Separate the solutions

x_{1} = \frac{- ( - π c ^{2} d ^{2} ) + c d π ^{2} c ^{2} d ^{2} + 4 y ^{9}}{2 d ^{2}}, x_{2} = \frac{- ( - π c ^{2} d ^{2} ) - c d π ^{2} c ^{2} d ^{2} + 4 y ^{9}}{2 d ^{2}}

x = \frac{- ( - π c ^{2} d ^{2} ) + c d π ^{2} c ^{2} d ^{2} + 4 y ^{9}}{2 d ^{2}} : \frac{c ( π c d + 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}

x = \frac{- ( - π c ^{2} d ^{2} ) - c d π ^{2} c ^{2} d ^{2} + 4 y ^{9}}{2 d ^{2}} : \frac{c ( π c d - 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}

حلول المعادلة التربيعيّة هي

x = \frac{c ( π c d + 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}, x = \frac{c ( π c d - 4 y ^{9} + π ^{2} c ^{2} d ^{2} )}{2 d}; d \neq = 0

39 x^{2} - 83 x = 56

(2 - x) (4 - x) + 2 = 0

- 12 x - x^{2} = 0

2 x^{2} - 12 x + 1 = 15

x^{2} - \frac{x}{3} = 0