Réitigh 20^2+left(1.5tright)^2-left(12+1.5tright)^2/60t=frac{34^2+{left(1.5tright)}^2-{left(30+1.5tright)}^2}{-102t}

$$\frac{ { 20 }^{ 2 } + { \left(1.5t \right) }^{ 2 } - { \left(12+1.5t \right) }^{ 2 } }{ 60t } = \frac{ { 34 }^{ 2 } + { \left(1.5t \right) }^{ 2 } - { \left(30+1.5t \right) }^{ 2 } }{ -102t }$$

Réitigh do t.

$$t = \frac{32}{7} = 4\frac{4}{7} \approx 4.571428571$$

Céimeanna chun Cothromóidí Líneacha a Réiteach

Ní féidir leis an athróg t a bheith comhionann le 0 toisc nach bhfuil an roinnt faoi nialas sainithe. Iolraigh an dá thaobh den chothromóid faoi 1020t, an comhiolraí is lú de 60t,-102t.

$$17\left(20^{2}+\left(1.5t\right)^{2}-\left(12+1.5t\right)^{2}\right)=-10\left(34^{2}+\left(1.5t\right)^{2}-\left(30+1.5t\right)^{2}\right)$$

Ríomh cumhacht 20 de 2 agus faigh 400.

$$17\left(400+\left(1.5t\right)^{2}-\left(12+1.5t\right)^{2}\right)=-10\left(34^{2}+\left(1.5t\right)^{2}-\left(30+1.5t\right)^{2}\right)$$

Fairsingigh \left(1.5t\right)^{2}

$$17\left(400+1.5^{2}t^{2}-\left(12+1.5t\right)^{2}\right)=-10\left(34^{2}+\left(1.5t\right)^{2}-\left(30+1.5t\right)^{2}\right)$$

Ríomh cumhacht 1.5 de 2 agus faigh 2.25.

$$17\left(400+2.25t^{2}-\left(12+1.5t\right)^{2}\right)=-10\left(34^{2}+\left(1.5t\right)^{2}-\left(30+1.5t\right)^{2}\right)$$

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(12+1.5t\right)^{2} a leathnú.

$$17\left(400+2.25t^{2}-\left(144+36t+2.25t^{2}\right)\right)=-10\left(34^{2}+\left(1.5t\right)^{2}-\left(30+1.5t\right)^{2}\right)$$

Chun an mhalairt ar 144+36t+2.25t^{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$17\left(400+2.25t^{2}-144-36t-2.25t^{2}\right)=-10\left(34^{2}+\left(1.5t\right)^{2}-\left(30+1.5t\right)^{2}\right)$$

Dealaigh 144 ó 400 chun 256 a fháil.

$$17\left(256+2.25t^{2}-36t-2.25t^{2}\right)=-10\left(34^{2}+\left(1.5t\right)^{2}-\left(30+1.5t\right)^{2}\right)$$

Comhcheangail 2.25t^{2} agus -2.25t^{2} chun 0 a fháil.

$$17\left(256-36t\right)=-10\left(34^{2}+\left(1.5t\right)^{2}-\left(30+1.5t\right)^{2}\right)$$

Úsáid an t-airí dáileach chun 17 a mhéadú faoi 256-36t.

$$4352-612t=-10\left(34^{2}+\left(1.5t\right)^{2}-\left(30+1.5t\right)^{2}\right)$$

Ríomh cumhacht 34 de 2 agus faigh 1156.

$$4352-612t=-10\left(1156+\left(1.5t\right)^{2}-\left(30+1.5t\right)^{2}\right)$$

Fairsingigh \left(1.5t\right)^{2}

$$4352-612t=-10\left(1156+1.5^{2}t^{2}-\left(30+1.5t\right)^{2}\right)$$

Ríomh cumhacht 1.5 de 2 agus faigh 2.25.

$$4352-612t=-10\left(1156+2.25t^{2}-\left(30+1.5t\right)^{2}\right)$$

Úsáid an teoirim dhéthéarmach \left(a+b\right)^{2}=a^{2}+2ab+b^{2} chun \left(30+1.5t\right)^{2} a leathnú.

$$4352-612t=-10\left(1156+2.25t^{2}-\left(900+90t+2.25t^{2}\right)\right)$$

Chun an mhalairt ar 900+90t+2.25t^{2} a aimsiú, aimsigh an mhalairt ar gach téarma.

$$4352-612t=-10\left(1156+2.25t^{2}-900-90t-2.25t^{2}\right)$$

Dealaigh 900 ó 1156 chun 256 a fháil.

$$4352-612t=-10\left(256+2.25t^{2}-90t-2.25t^{2}\right)$$

Comhcheangail 2.25t^{2} agus -2.25t^{2} chun 0 a fháil.

$$4352-612t=-10\left(256-90t\right)$$

Úsáid an t-airí dáileach chun -10 a mhéadú faoi 256-90t.

$$4352-612t=-2560+900t$$

Bain 900t ón dá thaobh.

$$4352-612t-900t=-2560$$

Comhcheangail -612t agus -900t chun -1512t a fháil.

$$4352-1512t=-2560$$

Bain 4352 ón dá thaobh.

$$-1512t=-2560-4352$$

Dealaigh 4352 ó -2560 chun -6912 a fháil.

$$-1512t=-6912$$

Roinn an dá thaobh faoi -1512.

$$t=\frac{-6912}{-1512}$$

Laghdaigh an codán \frac{-6912}{-1512} chuig na téarmaí is ísle trí -216 a bhaint agus a chealú.

$$t=\frac{32}{7}$$