Lahenda 20^2+left(15tright)^2-left(12+15tright)^2/60t=frac{34^2+{left(15tright)}^2-{left(30+15tright)}^2}{-102t}

$$\frac{ { 20 }^{ 2 } + { \left(15t \right) }^{ 2 } - { \left(12+15t \right) }^{ 2 } }{ 60t } = \frac{ { 34 }^{ 2 } + { \left(15t \right) }^{ 2 } - { \left(30+15t \right) }^{ 2 } }{ -102t }$$

Lahendage ja leidke t

$$t=\frac{16}{35}\approx 0,457142857$$

Juhised lineaarvõrrandi lahendamiseks

Muutuja t ei tohi võrduda väärtusega 0, kuna nulliga jagamist pole määratletud. Korrutage võrrandi mõlemad pooled arvuga 1020t, mis on arvu 60t,-102t vähim ühiskordne.

$$17\left(20^{2}+\left(15t\right)^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Arvutage 2 aste 20 ja leidke 400.

$$17\left(400+\left(15t\right)^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Laiendage \left(15t\right)^{2}.

$$17\left(400+15^{2}t^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Arvutage 2 aste 15 ja leidke 225.

$$17\left(400+225t^{2}-\left(12+15t\right)^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Kasutage kaksliikme \left(12+15t\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

$$17\left(400+225t^{2}-\left(144+360t+225t^{2}\right)\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Avaldise "144+360t+225t^{2}" vastandi leidmiseks tuleb leida iga liikme vastand.

$$17\left(400+225t^{2}-144-360t-225t^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Lahutage 144 väärtusest 400, et leida 256.

$$17\left(256+225t^{2}-360t-225t^{2}\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Kombineerige 225t^{2} ja -225t^{2}, et leida 0.

$$17\left(256-360t\right)=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Kasutage distributiivsusomadust, et korrutada 17 ja 256-360t.

$$4352-6120t=-10\left(34^{2}+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Arvutage 2 aste 34 ja leidke 1156.

$$4352-6120t=-10\left(1156+\left(15t\right)^{2}-\left(30+15t\right)^{2}\right)$$

Laiendage \left(15t\right)^{2}.

$$4352-6120t=-10\left(1156+15^{2}t^{2}-\left(30+15t\right)^{2}\right)$$

Arvutage 2 aste 15 ja leidke 225.

$$4352-6120t=-10\left(1156+225t^{2}-\left(30+15t\right)^{2}\right)$$

Kasutage kaksliikme \left(30+15t\right)^{2} arendamiseks binoomvalemit \left(a+b\right)^{2}=a^{2}+2ab+b^{2}.

$$4352-6120t=-10\left(1156+225t^{2}-\left(900+900t+225t^{2}\right)\right)$$

Avaldise "900+900t+225t^{2}" vastandi leidmiseks tuleb leida iga liikme vastand.

$$4352-6120t=-10\left(1156+225t^{2}-900-900t-225t^{2}\right)$$

Lahutage 900 väärtusest 1156, et leida 256.

$$4352-6120t=-10\left(256+225t^{2}-900t-225t^{2}\right)$$

Kombineerige 225t^{2} ja -225t^{2}, et leida 0.

$$4352-6120t=-10\left(256-900t\right)$$

Kasutage distributiivsusomadust, et korrutada -10 ja 256-900t.

$$4352-6120t=-2560+9000t$$

Lahutage mõlemast poolest 9000t.

$$4352-6120t-9000t=-2560$$

Kombineerige -6120t ja -9000t, et leida -15120t.

$$4352-15120t=-2560$$

Lahutage mõlemast poolest 4352.

$$-15120t=-2560-4352$$

Lahutage 4352 väärtusest -2560, et leida -6912.

$$-15120t=-6912$$

Jagage mõlemad pooled -15120-ga.

$$t=\frac{-6912}{-15120}$$

Taandage murd \frac{-6912}{-15120} vähimale ühiskordsele, eraldades ja taandades arvu -432.

$$t=\frac{16}{35}$$