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Phổ biến >

6x19^2-174x^{19}+1140=0

Lời Giải

6 x 1 9^{2} - 174 x^{19} + 1140 = 0

Lời Giải

x \approx - 1.11002 \dots, x \approx - 0.52631 \dots, x \approx 1.17428 \dots

Các bước giải pháp

6 x \cdot 1 9^{2} - 174 x^{19} + 1140 = 0

Mở rộng

6 x \cdot 1 9^{2} - 174 x^{19} + 1140 : 2166 x - 174 x^{19} + 1140

2166 x - 174 x^{19} + 1140 = 0

Viết ở dạng chuẩn

a_{n} x^{n} + \dots + a_{1} x + a_{0} = 0

- 174 x^{19} + 2166 x + 1140 = 0

Tìm một lời giải cho

- 174 x^{19} + 2166 x + 1140 = 0

bằng Newton-Raphson:

x \approx - 1.11002 \dots

Áp dụng phép chia số lớn:

\frac{- 174 x ^{19} + 2166 x + 1140}{x + 1.11002 \dots} = - 174 x^{18} + 193.14391 \dots x^{17} - 214.39409 \dots x^{16} + 237.98226 \dots x^{15} - 264.16567 \dots x^{14} + 293.22984 \dots x^{13} - 325.49172 \dots x^{12} + 361.30313 \dots x^{11} - 401.05461 \dots x^{10} + 445.17964 \dots x^{9} - 494.15942 \dots x^{8} + 548.52808 \dots x^{7} - 608.87852 \dots x^{6} + 675.86886 \dots x^{5} - 750.22964 \dots x^{4} + 832.77179 \dots x^{3} - 924.39543 \dots x^{2} + 1026.09973 \dots x + 1027.00620 \dots

- 174 x^{18} + 193.14391 \dots x^{17} - 214.39409 \dots x^{16} + 237.98226 \dots x^{15} - 264.16567 \dots x^{14} + 293.22984 \dots x^{13} - 325.49172 \dots x^{12} + 361.30313 \dots x^{11} - 401.05461 \dots x^{10} + 445.17964 \dots x^{9} - 494.15942 \dots x^{8} + 548.52808 \dots x^{7} - 608.87852 \dots x^{6} + 675.86886 \dots x^{5} - 750.22964 \dots x^{4} + 832.77179 \dots x^{3} - 924.39543 \dots x^{2} + 1026.09973 \dots x + 1027.00620 \dots \approx 0

Tìm một lời giải cho

- 174 x^{18} + 193.14391 \dots x^{17} - 214.39409 \dots x^{16} + 237.98226 \dots x^{15} - 264.16567 \dots x^{14} + 293.22984 \dots x^{13} - 325.49172 \dots x^{12} + 361.30313 \dots x^{11} - 401.05461 \dots x^{10} + 445.17964 \dots x^{9} - 494.15942 \dots x^{8} + 548.52808 \dots x^{7} - 608.87852 \dots x^{6} + 675.86886 \dots x^{5} - 750.22964 \dots x^{4} + 832.77179 \dots x^{3} - 924.39543 \dots x^{2} + 1026.09973 \dots x + 1027.00620 \dots = 0

bằng Newton-Raphson:

x \approx - 0.52631 \dots

Áp dụng phép chia số lớn:

\frac{- 174 x ^{18} + 193.14391 \dots x ^{17} - 214.39409 \dots x ^{16} + 237.98226 \dots x ^{15} - 264.16567 \dots x ^{14} + 293.22984 \dots x ^{13} - 325.49172 \dots x ^{12} + 361.30313 \dots x ^{11} - 401.05461 \dots x ^{10} + 445.17964 \dots x ^{9} - 494.15942 \dots x ^{8} + 548.52808 \dots x ^{7} - 608.87852 \dots x ^{6} + 675.86886 \dots x ^{5} - 750.22964 \dots x ^{4} + 832.77179 \dots x ^{3} - 924.39543 \dots x ^{2} + 1026.09973 \dots x + 1027.00620 \dots}{x + 0.52631 \dots} = - 174 x^{17} + 284.72293 \dots x^{16} - 364.24838 \dots x^{15} + 429.69209 \dots x^{14} - 490.31958 \dots x^{13} + 551.29297 \dots x^{12} - 615.64614 \dots x^{11} + 685.32767 \dots x^{10} - 761.75367 \dots x^{9} + 846.10294 \dots x^{8} - 939.47711 \dots x^{7} + 1042.99010 \dots x^{6} - 1157.82110 \dots x^{5} + 1285.24886 \dots x^{4} - 1426.67693 \dots x^{3} + 1583.65497 \dots x^{2} - 1757.89869 \dots x + 1951.31028 \dots

- 174 x^{17} + 284.72293 \dots x^{16} - 364.24838 \dots x^{15} + 429.69209 \dots x^{14} - 490.31958 \dots x^{13} + 551.29297 \dots x^{12} - 615.64614 \dots x^{11} + 685.32767 \dots x^{10} - 761.75367 \dots x^{9} + 846.10294 \dots x^{8} - 939.47711 \dots x^{7} + 1042.99010 \dots x^{6} - 1157.82110 \dots x^{5} + 1285.24886 \dots x^{4} - 1426.67693 \dots x^{3} + 1583.65497 \dots x^{2} - 1757.89869 \dots x + 1951.31028 \dots \approx 0

Tìm một lời giải cho

- 174 x^{17} + 284.72293 \dots x^{16} - 364.24838 \dots x^{15} + 429.69209 \dots x^{14} - 490.31958 \dots x^{13} + 551.29297 \dots x^{12} - 615.64614 \dots x^{11} + 685.32767 \dots x^{10} - 761.75367 \dots x^{9} + 846.10294 \dots x^{8} - 939.47711 \dots x^{7} + 1042.99010 \dots x^{6} - 1157.82110 \dots x^{5} + 1285.24886 \dots x^{4} - 1426.67693 \dots x^{3} + 1583.65497 \dots x^{2} - 1757.89869 \dots x + 1951.31028 \dots = 0

bằng Newton-Raphson:

x \approx 1.17428 \dots

Áp dụng phép chia số lớn:

\frac{- 174 x ^{17} + 284.72293 \dots x ^{16} - 364.24838 \dots x ^{15} + 429.69209 \dots x ^{14} - 490.31958 \dots x ^{13} + 551.29297 \dots x ^{12} - 615.64614 \dots x ^{11} + 685.32767 \dots x ^{10} - 761.75367 \dots x ^{9} + 846.10294 \dots x ^{8} - 939.47711 \dots x ^{7} + 1042.99010 \dots x ^{6} - 1157.82110 \dots x ^{5} + 1285.24886 \dots x ^{4} - 1426.67693 \dots x ^{3} + 1583.65497 \dots x ^{2} - 1757.89869 \dots x + 1951.31028 \dots}{x - 1.17428 \dots} = - 174 x^{16} + 80.39696 \dots x^{15} - 269.83926 \dots x^{14} + 112.82330 \dots x^{13} - 357.83261 \dots x^{12} + 131.09471 \dots x^{11} - 461.70329 \dots x^{10} + 143.15540 \dots x^{9} - 593.64811 \dots x^{8} + 148.98957 \dots x^{7} - 764.52056 \dots x^{6} + 145.22340 \dots x^{5} - 987.28712 \dots x^{4} + 125.89023 \dots x^{3} - 1278.84564 \dots x^{2} + 81.92291 \dots x - 1661.69766 \dots

- 174 x^{16} + 80.39696 \dots x^{15} - 269.83926 \dots x^{14} + 112.82330 \dots x^{13} - 357.83261 \dots x^{12} + 131.09471 \dots x^{11} - 461.70329 \dots x^{10} + 143.15540 \dots x^{9} - 593.64811 \dots x^{8} + 148.98957 \dots x^{7} - 764.52056 \dots x^{6} + 145.22340 \dots x^{5} - 987.28712 \dots x^{4} + 125.89023 \dots x^{3} - 1278.84564 \dots x^{2} + 81.92291 \dots x - 1661.69766 \dots \approx 0

Tìm một lời giải cho

- 174 x^{16} + 80.39696 \dots x^{15} - 269.83926 \dots x^{14} + 112.82330 \dots x^{13} - 357.83261 \dots x^{12} + 131.09471 \dots x^{11} - 461.70329 \dots x^{10} + 143.15540 \dots x^{9} - 593.64811 \dots x^{8} + 148.98957 \dots x^{7} - 764.52056 \dots x^{6} + 145.22340 \dots x^{5} - 987.28712 \dots x^{4} + 125.89023 \dots x^{3} - 1278.84564 \dots x^{2} + 81.92291 \dots x - 1661.69766 \dots = 0

bằng Newton-Raphson:

Không có nghiệm cho

x \in R

Các lời giải là

x \approx - 1.11002 \dots, x \approx - 0.52631 \dots, x \approx 1.17428 \dots

Đồ Thị

Ví dụ phổ biến

x^{4} + x - 6 = 0

y^{3} + y^{2} - 30 y = 0

3(2+4n)=3x^2+3x^4n

3 (2 + 4 n) = 3 x^{2} + 3 x^{4} n

x^2*x^2-2x^2+2=0

x^{2} \cdot x^{2} - 2 x^{2} + 2 = 0

solvefor t,y=(7-t^4)^2+2 giải cho

t, y = (7 - t^{4})^{2} + 2