Resolver (23!*17!*19!*15!)=(506*323)*x*20!*14!*18!*16!

$$(23 ! \times 17 ! \times 19 ! \times 15 ! )=(506 \times 323) \times x \times 20 ! \times 14 ! \times 18 ! \times 16 !$$

Resolver x

$$x=315$$

Pasos para resolver unha ecuación lineal

O factor de 23 é 25852016738884976640000.

$$25852016738884976640000\times 17!\times 19!\times 15!=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

O factor de 17 é 355687428096000.

$$25852016738884976640000\times 355687428096000\times 19!\times 15!=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

Multiplica 25852016738884976640000 e 355687428096000 para obter 9195237344948738535854639677440000000.

$$9195237344948738535854639677440000000\times 19!\times 15!=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

O factor de 19 é 121645100408832000.

$$9195237344948738535854639677440000000\times 121645100408832000\times 15!=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

Multiplica 9195237344948738535854639677440000000 e 121645100408832000 para obter 1118555570109331068277973902116680592607150080000000000.

$$1118555570109331068277973902116680592607150080000000000\times 15!=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

O factor de 15 é 1307674368000.

$$1118555570109331068277973902116680592607150080000000000\times 1307674368000=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

Multiplica 1118555570109331068277973902116680592607150080000000000 e 1307674368000 para obter 1462706448215599195613164370770924156195420453145149440000000000000.

$$1462706448215599195613164370770924156195420453145149440000000000000=506\times 323x\times 20!\times 14!\times 18!\times 16!$$

Multiplica 506 e 323 para obter 163438.

$$1462706448215599195613164370770924156195420453145149440000000000000=163438x\times 20!\times 14!\times 18!\times 16!$$

O factor de 20 é 2432902008176640000.

$$1462706448215599195613164370770924156195420453145149440000000000000=163438x\times 2432902008176640000\times 14!\times 18!\times 16!$$

Multiplica 163438 e 2432902008176640000 para obter 397628638412373688320000.

$$1462706448215599195613164370770924156195420453145149440000000000000=397628638412373688320000x\times 14!\times 18!\times 16!$$

O factor de 14 é 87178291200.

$$1462706448215599195613164370770924156195420453145149440000000000000=397628638412373688320000x\times 87178291200\times 18!\times 16!$$

Multiplica 397628638412373688320000 e 87178291200 para obter 34664585228973419083578998784000000.

$$1462706448215599195613164370770924156195420453145149440000000000000=34664585228973419083578998784000000x\times 18!\times 16!$$

O factor de 18 é 6402373705728000.

$$1462706448215599195613164370770924156195420453145149440000000000000=34664585228973419083578998784000000x\times 6402373705728000\times 16!$$

Multiplica 34664585228973419083578998784000000 e 6402373705728000 para obter 221935628989946640531344028197754085834752000000000.

$$1462706448215599195613164370770924156195420453145149440000000000000=221935628989946640531344028197754085834752000000000x\times 16!$$

O factor de 16 é 20922789888000.

$$1462706448215599195613164370770924156195420453145149440000000000000=221935628989946640531344028197754085834752000000000x\times 20922789888000$$

Multiplica 221935628989946640531344028197754085834752000000000 e 20922789888000 para obter 4643512534017775224168775780225156051414033184587776000000000000.

$$1462706448215599195613164370770924156195420453145149440000000000000=4643512534017775224168775780225156051414033184587776000000000000x$$

Cambia de lado para que todos os termos variables estean no lado esquerdo.

$$4643512534017775224168775780225156051414033184587776000000000000x=1462706448215599195613164370770924156195420453145149440000000000000$$

Divide ambos lados entre 4643512534017775224168775780225156051414033184587776000000000000.

$$x=\frac{1462706448215599195613164370770924156195420453145149440000000000000}{4643512534017775224168775780225156051414033184587776000000000000}$$

Divide 1462706448215599195613164370770924156195420453145149440000000000000 entre 4643512534017775224168775780225156051414033184587776000000000000 para obter 315.

$$x=315$$