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人気のある代数 >

4.7x10^1=4.7x^{10}

解

4.7 x 1 0^{1} = 4.7 x^{10}

解

x = 0, x = 1.29154 \dots, x = - \frac{1.82165 \dots}{2.82088 \dots} + i \frac{9.95528 \dots}{2.82088 \dots}, x = - \frac{1.82165 \dots}{2.82088 \dots} - i \frac{9.95528 \dots}{2.82088 \dots}, x = 6 4.64158 \dots cos (\frac{2 π}{9}) + 6 4.64158 \dots i sin (\frac{2 π}{9}), x = 6 4.64158 \dots cos (\frac{8 π}{9}) + 6 4.64158 \dots i sin (\frac{8 π}{9}), x = 6 4.64158 \dots cos (\frac{14 π}{9}) + 6 4.64158 \dots i sin (\frac{14 π}{9}), x = 6 4.64158 \dots cos (\frac{2 π}{9}) - 6 4.64158 \dots i sin (\frac{2 π}{9}), x = 6 4.64158 \dots cos (\frac{4 π}{9}) + 6 4.64158 \dots i sin (\frac{4 π}{9}), x = 6 4.64158 \dots cos (\frac{10 π}{9}) + 6 4.64158 \dots i sin (\frac{10 π}{9})

解答ステップ

4.7 x \cdot 1 0^{1} = 4.7 x^{10}

4.7 x^{10}

を左側に移動します

4.7 x \cdot 1 0^{1} - 4.7 x^{10} = 0

因数

4.7 x \cdot 1 0^{1} - 4.7 x^{10} : - x (9 4.7 x - 947) (4. 7^{\frac{2}{9}} x^{2} + 9 220.9 x + 4 7^{\frac{2}{9}}) (4. 7^{\frac{2}{3}} x^{6} + 3 220.9 x^{3} + 4 7^{\frac{2}{3}})

- x (9 4.7 x - 947) (4. 7^{\frac{2}{9}} x^{2} + 9 220.9 x + 4 7^{\frac{2}{9}}) (4. 7^{\frac{2}{3}} x^{6} + 3 220.9 x^{3} + 4 7^{\frac{2}{3}}) = 0

零因子の原則を使用:

ab = 0

ならば

a = 0

または

b = 0

x = 0 or 9 4.7 x - 947 = 0 or 4. 7^{\frac{2}{9}} x^{2} + 9 220.9 x + 4 7^{\frac{2}{9}} = 0 or 4. 7^{\frac{2}{3}} x^{6} + 3 220.9 x^{3} + 4 7^{\frac{2}{3}} = 0

解く

9 4.7 x - 947 = 0 : x = 1.29154 \dots

解く

4. 7^{\frac{2}{9}} x^{2} + 9 220.9 x + 4 7^{\frac{2}{9}} = 0 : x = - \frac{1.82165 \dots}{2.82088 \dots} + i \frac{9.95528 \dots}{2.82088 \dots}, x = - \frac{1.82165 \dots}{2.82088 \dots} - i \frac{9.95528 \dots}{2.82088 \dots}

解く

4. 7^{\frac{2}{3}} x^{6} + 3 220.9 x^{3} + 4 7^{\frac{2}{3}} = 0 : x = 6 4.64158 \dots cos (\frac{2 π}{9}) + 6 4.64158 \dots i sin (\frac{2 π}{9}), x = 6 4.64158 \dots cos (\frac{8 π}{9}) + 6 4.64158 \dots i sin (\frac{8 π}{9}), x = 6 4.64158 \dots cos (\frac{14 π}{9}) + 6 4.64158 \dots i sin (\frac{14 π}{9}), x = 6 4.64158 \dots cos (\frac{2 π}{9}) - 6 4.64158 \dots i sin (\frac{2 π}{9}), x = 6 4.64158 \dots cos (\frac{4 π}{9}) + 6 4.64158 \dots i sin (\frac{4 π}{9}), x = 6 4.64158 \dots cos (\frac{10 π}{9}) + 6 4.64158 \dots i sin (\frac{10 π}{9})

解答は

x = 0, x = 1.29154 \dots, x = - \frac{1.82165 \dots}{2.82088 \dots} + i \frac{9.95528 \dots}{2.82088 \dots}, x = - \frac{1.82165 \dots}{2.82088 \dots} - i \frac{9.95528 \dots}{2.82088 \dots}, x = 6 4.64158 \dots cos (\frac{2 π}{9}) + 6 4.64158 \dots i sin (\frac{2 π}{9}), x = 6 4.64158 \dots cos (\frac{8 π}{9}) + 6 4.64158 \dots i sin (\frac{8 π}{9}), x = 6 4.64158 \dots cos (\frac{14 π}{9}) + 6 4.64158 \dots i sin (\frac{14 π}{9}), x = 6 4.64158 \dots cos (\frac{2 π}{9}) - 6 4.64158 \dots i sin (\frac{2 π}{9}), x = 6 4.64158 \dots cos (\frac{4 π}{9}) + 6 4.64158 \dots i sin (\frac{4 π}{9}), x = 6 4.64158 \dots cos (\frac{10 π}{9}) + 6 4.64158 \dots i sin (\frac{10 π}{9})

グラフ

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