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

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

Lahendage ja leidke x

$$x=315$$

Juhised lineaarvõrrandi lahendamiseks

23 faktoriaal on 25852016738884976640000.

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

17 faktoriaal on 355687428096000.

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

Korrutage 25852016738884976640000 ja 355687428096000, et leida 9195237344948738535854639677440000000.

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

19 faktoriaal on 121645100408832000.

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

Korrutage 9195237344948738535854639677440000000 ja 121645100408832000, et leida 1118555570109331068277973902116680592607150080000000000.

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

15 faktoriaal on 1307674368000.

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

Korrutage 1118555570109331068277973902116680592607150080000000000 ja 1307674368000, et leida 1462706448215599195613164370770924156195420453145149440000000000000.

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

Korrutage 506 ja 323, et leida 163438.

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

20 faktoriaal on 2432902008176640000.

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

Korrutage 163438 ja 2432902008176640000, et leida 397628638412373688320000.

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

14 faktoriaal on 87178291200.

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

Korrutage 397628638412373688320000 ja 87178291200, et leida 34664585228973419083578998784000000.

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

18 faktoriaal on 6402373705728000.

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

Korrutage 34664585228973419083578998784000000 ja 6402373705728000, et leida 221935628989946640531344028197754085834752000000000.

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

16 faktoriaal on 20922789888000.

$$1462706448215599195613164370770924156195420453145149440000000000000=221935628989946640531344028197754085834752000000000x\times 20922789888000$$

Korrutage 221935628989946640531344028197754085834752000000000 ja 20922789888000, et leida 4643512534017775224168775780225156051414033184587776000000000000.

$$1462706448215599195613164370770924156195420453145149440000000000000=4643512534017775224168775780225156051414033184587776000000000000x$$

Vahetage pooled nii, et kõik muutuvad liikmed asuksid vasakul.

$$4643512534017775224168775780225156051414033184587776000000000000x=1462706448215599195613164370770924156195420453145149440000000000000$$

Jagage mõlemad pooled 4643512534017775224168775780225156051414033184587776000000000000-ga.

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

Jagage 1462706448215599195613164370770924156195420453145149440000000000000 väärtusega 4643512534017775224168775780225156051414033184587776000000000000, et leida 315.

$$x=315$$