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인기 있는 대수학 >

25x(10x^{12})=(25x^{10})x^{12}

해법

25 x (10 x^{12}) = (25 x^{10}) x^{12}

해법

x = 0, x = 910, x = - 9 \frac{5}{256} + i \frac{3 1 0 ^{\frac{2}{9}}}{2}, x = - 9 \frac{5}{256} - i \frac{3 1 0 ^{\frac{2}{9}}}{2}, x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{8 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{8 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{14 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{14 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) - i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{4 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{4 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{10 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{10 π}{9})

솔루션 단계

25 x (10 x^{12}) = (25 x^{10}) x^{12}

(25 x^{10}) x^{12}

를 왼쪽으로 이동

25 x \cdot 10 x^{12} - 25 x^{10} x^{12} = 0

25 x \cdot 10 x^{12} - 25 x^{10} x^{12}

인수 :

- 25 x^{13} (x - 910) (x^{2} + 910 x + 1 0^{\frac{2}{9}}) (x^{6} + 310 x^{3} + 1 0^{\frac{2}{3}})

- 25 x^{13} (x - 910) (x^{2} + 910 x + 1 0^{\frac{2}{9}}) (x^{6} + 310 x^{3} + 1 0^{\frac{2}{3}}) = 0

제로 인자 원리 사용:\4각형이면

ab = 0

그렇다면

a = 0

or

b = 0

x = 0 or x - 910 = 0 or x^{2} + 910 x + 1 0^{\frac{2}{9}} = 0 or x^{6} + 310 x^{3} + 1 0^{\frac{2}{3}} = 0

x - 910 = 0

해결 :

x = 910

x^{2} + 910 x + 1 0^{\frac{2}{9}} = 0

해결 :

x = - 9 \frac{5}{256} + i \frac{3 1 0 ^{\frac{2}{9}}}{2}, x = - 9 \frac{5}{256} - i \frac{3 1 0 ^{\frac{2}{9}}}{2}

x^{6} + 310 x^{3} + 1 0^{\frac{2}{3}} = 0

해결 :

x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{8 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{8 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{14 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{14 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) - i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{4 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{4 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{10 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{10 π}{9})

해결책은

x = 0, x = 910, x = - 9 \frac{5}{256} + i \frac{3 1 0 ^{\frac{2}{9}}}{2}, x = - 9 \frac{5}{256} - i \frac{3 1 0 ^{\frac{2}{9}}}{2}, x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{8 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{8 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{14 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{14 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{2 π}{9}) - i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{2 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{4 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{4 π}{9}), x = 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} cos (\frac{10 π}{9}) + i 6 \frac{2 ^{\frac{2}{3}} ( 3 \cdot 5 ^{\frac{2}{3}} + 2 3 2 ( \frac{5}{4} ) ^{\frac{2}{3}} )}{4} sin (\frac{10 π}{9})

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