Whakaoti i te y=sqrt{(26-3y/frac{4{3}}+2y)*26-3y/4}

$$y= \sqrt{ ( \frac{ 26-3y }{ \frac{ 4 }{ 3 } } +2y) \times \frac{ 26-3y }{ 4 } }$$

Whakaoti mō y

$$y=6$$

Ngā Upane Otinga

Pūruatia ngā taha e rua o te whārite.

$$y^{2}=\left(\sqrt{\left(\frac{26-3y}{\frac{4}{3}}+2y\right)\times \frac{26-3y}{4}}\right)^{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te \frac{26-3y}{\frac{4}{3}}+2y ki te \frac{26-3y}{4}.

$$y^{2}=\left(\sqrt{\frac{26-3y}{\frac{4}{3}}\times \frac{26-3y}{4}+2y\times \frac{26-3y}{4}}\right)^{2}$$

Whakakorea atu te tauwehe pūnoa nui rawa 4 i roto i te 2 me te 4.

$$y^{2}=\left(\sqrt{\frac{26-3y}{\frac{4}{3}}\times \frac{26-3y}{4}+\frac{26-3y}{2}y}\right)^{2}$$

Tuhia te \frac{26-3y}{2}y hei hautanga kotahi.

$$y^{2}=\left(\sqrt{\frac{26-3y}{\frac{4}{3}}\times \frac{26-3y}{4}+\frac{\left(26-3y\right)y}{2}}\right)^{2}$$

Tātaihia te \sqrt{\frac{26-3y}{\frac{4}{3}}\times \frac{26-3y}{4}+\frac{\left(26-3y\right)y}{2}} mā te pū o 2, kia riro ko \frac{26-3y}{\frac{4}{3}}\times \frac{26-3y}{4}+\frac{\left(26-3y\right)y}{2}.

$$y^{2}=\frac{26-3y}{\frac{4}{3}}\times \frac{26-3y}{4}+\frac{\left(26-3y\right)y}{2}$$

Whakawehea ia wā o 26-3y ki te \frac{4}{3}, kia riro ko \frac{26}{\frac{4}{3}}+\frac{-3y}{\frac{4}{3}}.

$$y^{2}=\left(\frac{26}{\frac{4}{3}}+\frac{-3y}{\frac{4}{3}}\right)\times \frac{26-3y}{4}+\frac{\left(26-3y\right)y}{2}$$

Whakawehe 26 ki te \frac{4}{3} mā te whakarea 26 ki te tau huripoki o \frac{4}{3}.

$$y^{2}=\left(26\times \frac{3}{4}+\frac{-3y}{\frac{4}{3}}\right)\times \frac{26-3y}{4}+\frac{\left(26-3y\right)y}{2}$$

Tuhia te 26\times \frac{3}{4} hei hautanga kotahi.

$$y^{2}=\left(\frac{26\times 3}{4}+\frac{-3y}{\frac{4}{3}}\right)\times \frac{26-3y}{4}+\frac{\left(26-3y\right)y}{2}$$

Whakareatia te 26 ki te 3, ka 78.

$$y^{2}=\left(\frac{78}{4}+\frac{-3y}{\frac{4}{3}}\right)\times \frac{26-3y}{4}+\frac{\left(26-3y\right)y}{2}$$

Whakahekea te hautanga \frac{78}{4} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 2.

$$y^{2}=\left(\frac{39}{2}+\frac{-3y}{\frac{4}{3}}\right)\times \frac{26-3y}{4}+\frac{\left(26-3y\right)y}{2}$$

Whakawehea te -3y ki te \frac{4}{3}, kia riro ko -\frac{9}{4}y.

$$y^{2}=\left(\frac{39}{2}-\frac{9}{4}y\right)\times \frac{26-3y}{4}+\frac{\left(26-3y\right)y}{2}$$

Whakawehea ia wā o 26-3y ki te 4, kia riro ko \frac{13}{2}-\frac{3}{4}y.

$$y^{2}=\left(\frac{39}{2}-\frac{9}{4}y\right)\left(\frac{13}{2}-\frac{3}{4}y\right)+\frac{\left(26-3y\right)y}{2}$$

Me hoatu te āhuatanga tohatoha mā te whakarea ia tau o \frac{39}{2}-\frac{9}{4}y ki ia tau o \frac{13}{2}-\frac{3}{4}y.

$$y^{2}=\frac{39}{2}\times \frac{13}{2}+\frac{39}{2}\left(-\frac{3}{4}\right)y-\frac{9}{4}y\times \frac{13}{2}-\frac{9}{4}y\left(-\frac{3}{4}\right)y+\frac{\left(26-3y\right)y}{2}$$

Whakareatia te y ki te y, ka y^{2}.

$$y^{2}=\frac{39}{2}\times \frac{13}{2}+\frac{39}{2}\left(-\frac{3}{4}\right)y-\frac{9}{4}y\times \frac{13}{2}-\frac{9}{4}y^{2}\left(-\frac{3}{4}\right)+\frac{\left(26-3y\right)y}{2}$$

Me whakarea te \frac{39}{2} ki te \frac{13}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$y^{2}=\frac{39\times 13}{2\times 2}+\frac{39}{2}\left(-\frac{3}{4}\right)y-\frac{9}{4}y\times \frac{13}{2}-\frac{9}{4}y^{2}\left(-\frac{3}{4}\right)+\frac{\left(26-3y\right)y}{2}$$

Mahia ngā whakarea i roto i te hautanga \frac{39\times 13}{2\times 2}.

$$y^{2}=\frac{507}{4}+\frac{39}{2}\left(-\frac{3}{4}\right)y-\frac{9}{4}y\times \frac{13}{2}-\frac{9}{4}y^{2}\left(-\frac{3}{4}\right)+\frac{\left(26-3y\right)y}{2}$$

Me whakarea te \frac{39}{2} ki te -\frac{3}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$y^{2}=\frac{507}{4}+\frac{39\left(-3\right)}{2\times 4}y-\frac{9}{4}y\times \frac{13}{2}-\frac{9}{4}y^{2}\left(-\frac{3}{4}\right)+\frac{\left(26-3y\right)y}{2}$$

Mahia ngā whakarea i roto i te hautanga \frac{39\left(-3\right)}{2\times 4}.

$$y^{2}=\frac{507}{4}+\frac{-117}{8}y-\frac{9}{4}y\times \frac{13}{2}-\frac{9}{4}y^{2}\left(-\frac{3}{4}\right)+\frac{\left(26-3y\right)y}{2}$$

Ka taea te hautanga \frac{-117}{8} te tuhi anō ko -\frac{117}{8} mā te tango i te tohu tōraro.

$$y^{2}=\frac{507}{4}-\frac{117}{8}y-\frac{9}{4}y\times \frac{13}{2}-\frac{9}{4}y^{2}\left(-\frac{3}{4}\right)+\frac{\left(26-3y\right)y}{2}$$

Me whakarea te -\frac{9}{4} ki te \frac{13}{2} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$y^{2}=\frac{507}{4}-\frac{117}{8}y+\frac{-9\times 13}{4\times 2}y-\frac{9}{4}y^{2}\left(-\frac{3}{4}\right)+\frac{\left(26-3y\right)y}{2}$$

Mahia ngā whakarea i roto i te hautanga \frac{-9\times 13}{4\times 2}.

$$y^{2}=\frac{507}{4}-\frac{117}{8}y+\frac{-117}{8}y-\frac{9}{4}y^{2}\left(-\frac{3}{4}\right)+\frac{\left(26-3y\right)y}{2}$$

Ka taea te hautanga \frac{-117}{8} te tuhi anō ko -\frac{117}{8} mā te tango i te tohu tōraro.

$$y^{2}=\frac{507}{4}-\frac{117}{8}y-\frac{117}{8}y-\frac{9}{4}y^{2}\left(-\frac{3}{4}\right)+\frac{\left(26-3y\right)y}{2}$$

Pahekotia te -\frac{117}{8}y me -\frac{117}{8}y, ka -\frac{117}{4}y.

$$y^{2}=\frac{507}{4}-\frac{117}{4}y-\frac{9}{4}y^{2}\left(-\frac{3}{4}\right)+\frac{\left(26-3y\right)y}{2}$$

Me whakarea te -\frac{9}{4} ki te -\frac{3}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro.

$$y^{2}=\frac{507}{4}-\frac{117}{4}y+\frac{-9\left(-3\right)}{4\times 4}y^{2}+\frac{\left(26-3y\right)y}{2}$$

Mahia ngā whakarea i roto i te hautanga \frac{-9\left(-3\right)}{4\times 4}.

$$y^{2}=\frac{507}{4}-\frac{117}{4}y+\frac{27}{16}y^{2}+\frac{\left(26-3y\right)y}{2}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 26-3y ki te y.

$$y^{2}=\frac{507}{4}-\frac{117}{4}y+\frac{27}{16}y^{2}+\frac{26y-3y^{2}}{2}$$

Whakawehea ia wā o 26y-3y^{2} ki te 2, kia riro ko 13y-\frac{3}{2}y^{2}.

$$y^{2}=\frac{507}{4}-\frac{117}{4}y+\frac{27}{16}y^{2}+13y-\frac{3}{2}y^{2}$$

Pahekotia te -\frac{117}{4}y me 13y, ka -\frac{65}{4}y.

$$y^{2}=\frac{507}{4}-\frac{65}{4}y+\frac{27}{16}y^{2}-\frac{3}{2}y^{2}$$

Pahekotia te \frac{27}{16}y^{2} me -\frac{3}{2}y^{2}, ka \frac{3}{16}y^{2}.

$$y^{2}=\frac{507}{4}-\frac{65}{4}y+\frac{3}{16}y^{2}$$

Tangohia te \frac{507}{4} mai i ngā taha e rua.

$$y^{2}-\frac{507}{4}=-\frac{65}{4}y+\frac{3}{16}y^{2}$$

Me tāpiri te \frac{65}{4}y ki ngā taha e rua.

$$y^{2}-\frac{507}{4}+\frac{65}{4}y=\frac{3}{16}y^{2}$$

Tangohia te \frac{3}{16}y^{2} mai i ngā taha e rua.

$$y^{2}-\frac{507}{4}+\frac{65}{4}y-\frac{3}{16}y^{2}=0$$

Pahekotia te y^{2} me -\frac{3}{16}y^{2}, ka \frac{13}{16}y^{2}.

$$\frac{13}{16}y^{2}-\frac{507}{4}+\frac{65}{4}y=0$$

Ko ngā whārite katoa o te āhua ax^{2}+bx+c=0 ka taea te whakaoti mā te whakamahi i te tikanga tātai pūrua: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. E rua ngā otinga ka puta i te tikanga tātai pūrua, ko tētahi ina he tāpiri a ±, ā, ko tētahi ina he tango.

$$\frac{13}{16}y^{2}+\frac{65}{4}y-\frac{507}{4}=0$$

Kei te āhua arowhānui tēnei whārite: ax^{2}+bx+c=0. Me whakakapi \frac{13}{16} mō a, \frac{65}{4} mō b, me -\frac{507}{4} mō c i te tikanga tātai pūrua, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\frac{65}{4}±\sqrt{\left(\frac{65}{4}\right)^{2}-4\times \frac{13}{16}\left(-\frac{507}{4}\right)}}{2\times \frac{13}{16}}$$

Pūruatia \frac{65}{4} mā te pūrua i te taurunga me te tauraro o te hautanga.

$$y=\frac{-\frac{65}{4}±\sqrt{\frac{4225}{16}-4\times \frac{13}{16}\left(-\frac{507}{4}\right)}}{2\times \frac{13}{16}}$$

Whakareatia -4 ki te \frac{13}{16}.

$$y=\frac{-\frac{65}{4}±\sqrt{\frac{4225}{16}-\frac{13}{4}\left(-\frac{507}{4}\right)}}{2\times \frac{13}{16}}$$

Whakareatia -\frac{13}{4} ki te -\frac{507}{4} mā te whakarea taurunga ki te taurunga me te tauraro ki te tauraro, ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$y=\frac{-\frac{65}{4}±\sqrt{\frac{4225+6591}{16}}}{2\times \frac{13}{16}}$$

Tāpiri \frac{4225}{16} ki te \frac{6591}{16} mā te kimi i te tauraro pātahi me te tāpiri i ngā taurunga. Ka whakaiti i te hautanga ki ngā kīanga tau iti rawa e taea ana.

$$y=\frac{-\frac{65}{4}±\sqrt{676}}{2\times \frac{13}{16}}$$

Tuhia te pūtakerua o te 676.

$$y=\frac{-\frac{65}{4}±26}{2\times \frac{13}{16}}$$

Whakareatia 2 ki te \frac{13}{16}.

$$y=\frac{-\frac{65}{4}±26}{\frac{13}{8}}$$

Nā, me whakaoti te whārite y=\frac{-\frac{65}{4}±26}{\frac{13}{8}} ina he tāpiri te ±. Tāpiri -\frac{65}{4} ki te 26.

$$y=\frac{\frac{39}{4}}{\frac{13}{8}}$$

Whakawehe \frac{39}{4} ki te \frac{13}{8} mā te whakarea \frac{39}{4} ki te tau huripoki o \frac{13}{8}.

$$y=6$$

Nā, me whakaoti te whārite y=\frac{-\frac{65}{4}±26}{\frac{13}{8}} ina he tango te ±. Tango 26 mai i -\frac{65}{4}.

$$y=-\frac{\frac{169}{4}}{\frac{13}{8}}$$

Whakawehe -\frac{169}{4} ki te \frac{13}{8} mā te whakarea -\frac{169}{4} ki te tau huripoki o \frac{13}{8}.

$$y=-26$$

Kua oti te whārite te whakatau.

$$y=6 y=-26$$

Whakakapia te 6 mō te y i te whārite y=\sqrt{\left(\frac{26-3y}{\frac{4}{3}}+2y\right)\times \frac{26-3y}{4}}.

$$6=\sqrt{\left(\frac{26-3\times 6}{\frac{4}{3}}+2\times 6\right)\times \frac{26-3\times 6}{4}}$$

Whakarūnātia. Ko te uara y=6 kua ngata te whārite.

$$6=6$$

Whakakapia te -26 mō te y i te whārite y=\sqrt{\left(\frac{26-3y}{\frac{4}{3}}+2y\right)\times \frac{26-3y}{4}}.

$$-26=\sqrt{\left(\frac{26-3\left(-26\right)}{\frac{4}{3}}+2\left(-26\right)\right)\times \frac{26-3\left(-26\right)}{4}}$$

Whakarūnātia. Ko te uara y=-26 kāore e ngata ana ki te whārite nā te mea e rerekē ngā tohu o te taha maui me te taha katau.

$$-26=26$$

Ko te whārite y=\sqrt{\frac{26-3y}{4}\left(\frac{26-3y}{\frac{4}{3}}+2y\right)} he rongoā ahurei.

$$y=6$$