Réitigh left(x-3right)^2left(10-17xright)^2=0

$${ \left(x-3 \right) }^{ 2 } { \left(10-17x \right) }^{ 2 } = 0$$

Réitigh do x.

$$x=\frac{10}{17}\approx 0.588235294$$

$$x=3$$

Céimeanna Réitigh

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(x-3\right)^{2} a leathnú.

$$\left(x^{2}-6x+9\right)\left(10-17x\right)^{2}=0$$

Úsáid an teoirim dhéthéarmach \left(a-b\right)^{2}=a^{2}-2ab+b^{2} chun \left(10-17x\right)^{2} a leathnú.

$$\left(x^{2}-6x+9\right)\left(100-340x+289x^{2}\right)=0$$

Úsáid an t-airí dáileach chun x^{2}-6x+9 a mhéadú faoi 100-340x+289x^{2} agus chun téarmaí comhchosúla a chumasc.

$$4741x^{2}-2074x^{3}+289x^{4}-3660x+900=0$$

Atheagraigh an chothromóid lena cur i bhfoirm chaighdeánach. Cuir na téarmaí in ord ón gcumhacht is airde go dtí an chumhacht is ísle.

$$289x^{4}-2074x^{3}+4741x^{2}-3660x+900=0$$

Faoi theoirim na fréimhe cóimheasta, bíonn fréamhacha cóimheasta iltéarmaigh i bhfoirm \frac{p}{q}, nuair a roinneann p an téarma seasta 900 agus nuair a roinneann q an chomhéifeacht thosaigh 289. Liostaigh gach iarrthóir \frac{p}{q}.

$$±\frac{900}{289},±\frac{900}{17},±900,±\frac{450}{289},±\frac{450}{17},±450,±\frac{300}{289},±\frac{300}{17},±300,±\frac{225}{289},±\frac{225}{17},±225,±\frac{180}{289},±\frac{180}{17},±180,±\frac{150}{289},±\frac{150}{17},±150,±\frac{100}{289},±\frac{100}{17},±100,±\frac{90}{289},±\frac{90}{17},±90,±\frac{75}{289},±\frac{75}{17},±75,±\frac{60}{289},±\frac{60}{17},±60,±\frac{50}{289},±\frac{50}{17},±50,±\frac{45}{289},±\frac{45}{17},±45,±\frac{36}{289},±\frac{36}{17},±36,±\frac{30}{289},±\frac{30}{17},±30,±\frac{25}{289},±\frac{25}{17},±25,±\frac{20}{289},±\frac{20}{17},±20,±\frac{18}{289},±\frac{18}{17},±18,±\frac{15}{289},±\frac{15}{17},±15,±\frac{12}{289},±\frac{12}{17},±12,±\frac{10}{289},±\frac{10}{17},±10,±\frac{9}{289},±\frac{9}{17},±9,±\frac{6}{289},±\frac{6}{17},±6,±\frac{5}{289},±\frac{5}{17},±5,±\frac{4}{289},±\frac{4}{17},±4,±\frac{3}{289},±\frac{3}{17},±3,±\frac{2}{289},±\frac{2}{17},±2,±\frac{1}{289},±\frac{1}{17},±1$$

Is féidir fréamh den sórt sin a aimsiú ach triail a bhaint as na luachanna slánuimhreach ar fad, ag tosú leis an gceann is lú bunaithe ar an dearbhluach. Mura n-aimsítear fréamhacha slánuimhreach, bain triail as codáin.

$$x=3$$

Faoi theoirim an fhachtóra, is é x-k fachtóir an iltéarmaigh do gach fréamh k. Roinn 289x^{4}-2074x^{3}+4741x^{2}-3660x+900 faoi x-3 chun 289x^{3}-1207x^{2}+1120x-300 a fháil. Réitigh an chothromóid nuair is ionann an toradh agus 0.

$$289x^{3}-1207x^{2}+1120x-300=0$$

Faoi theoirim na fréimhe cóimheasta, bíonn fréamhacha cóimheasta iltéarmaigh i bhfoirm \frac{p}{q}, nuair a roinneann p an téarma seasta -300 agus nuair a roinneann q an chomhéifeacht thosaigh 289. Liostaigh gach iarrthóir \frac{p}{q}.

$$±\frac{300}{289},±\frac{300}{17},±300,±\frac{150}{289},±\frac{150}{17},±150,±\frac{100}{289},±\frac{100}{17},±100,±\frac{75}{289},±\frac{75}{17},±75,±\frac{60}{289},±\frac{60}{17},±60,±\frac{50}{289},±\frac{50}{17},±50,±\frac{30}{289},±\frac{30}{17},±30,±\frac{25}{289},±\frac{25}{17},±25,±\frac{20}{289},±\frac{20}{17},±20,±\frac{15}{289},±\frac{15}{17},±15,±\frac{12}{289},±\frac{12}{17},±12,±\frac{10}{289},±\frac{10}{17},±10,±\frac{6}{289},±\frac{6}{17},±6,±\frac{5}{289},±\frac{5}{17},±5,±\frac{4}{289},±\frac{4}{17},±4,±\frac{3}{289},±\frac{3}{17},±3,±\frac{2}{289},±\frac{2}{17},±2,±\frac{1}{289},±\frac{1}{17},±1$$

Is féidir fréamh den sórt sin a aimsiú ach triail a bhaint as na luachanna slánuimhreach ar fad, ag tosú leis an gceann is lú bunaithe ar an dearbhluach. Mura n-aimsítear fréamhacha slánuimhreach, bain triail as codáin.

$$x=3$$

Faoi theoirim an fhachtóra, is é x-k fachtóir an iltéarmaigh do gach fréamh k. Roinn 289x^{3}-1207x^{2}+1120x-300 faoi x-3 chun 289x^{2}-340x+100 a fháil. Réitigh an chothromóid nuair is ionann an toradh agus 0.

$$289x^{2}-340x+100=0$$

Is féidir gach cothromóid i bhfoirm ax^{2}+bx+c=0 a réiteach ach an fhoirmle chearnach seo a úsáid: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Cuir 289 in ionad a, -340 in ionad b agus 100 in ionad c san fhoirmle chearnach.

$$x=\frac{-\left(-340\right)±\sqrt{\left(-340\right)^{2}-4\times 289\times 100}}{2\times 289}$$

Déan áirimh.

$$x=\frac{340±0}{578}$$

Is ionann na réitigh.

$$x=\frac{10}{17}$$

Liostaigh na réitigh ar fad a aimsíodh.

$$x=3 x=\frac{10}{17}$$