Whakaoti i te x/3*3+x/4*4+x/6*5+(x/4-8)*2=50^4

$$\frac { x } { 3 } \times 3 + \frac { x } { 4 } \times 4 + \frac { x } { 6 } \times 5 + ( \frac { x } { 4 } - 8 ) \cdot 2 = 50 ^ { 4 }$$

Whakaoti mō x

$$x = \frac{9375024}{5} = 1875004\frac{4}{5} = 1875004.8$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Me whakarea ngā taha e rua o te whārite ki te 12, arā, te tauraro pātahi he tino iti rawa te kitea o 3,4,6.

$$4x\times 3+3x\times 4+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Whakareatia te 4 ki te 3, ka 12.

$$12x+3x\times 4+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Whakareatia te 3 ki te 4, ka 12.

$$12x+12x+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Pahekotia te 12x me 12x, ka 24x.

$$24x+2x\times 5+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Whakareatia te 2 ki te 5, ka 10.

$$24x+10x+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Pahekotia te 24x me 10x, ka 34x.

$$34x+12\left(\frac{x}{4}-8\right)\times 2=12\times 50^{4}$$

Whakareatia te 12 ki te 2, ka 24.

$$34x+24\left(\frac{x}{4}-8\right)=12\times 50^{4}$$

Whakamahia te āhuatanga tohatoha hei whakarea te 24 ki te \frac{x}{4}-8.

$$34x+24\times \frac{x}{4}-192=12\times 50^{4}$$

Whakakorea atu te tauwehe pūnoa nui rawa 4 i roto i te 24 me te 4.

$$34x+6x-192=12\times 50^{4}$$

Pahekotia te 34x me 6x, ka 40x.

$$40x-192=12\times 50^{4}$$

Tātaihia te 50 mā te pū o 4, kia riro ko 6250000.

$$40x-192=12\times 6250000$$

Whakareatia te 12 ki te 6250000, ka 75000000.

$$40x-192=75000000$$

Me tāpiri te 192 ki ngā taha e rua.

$$40x=75000000+192$$

Tāpirihia te 75000000 ki te 192, ka 75000192.

$$40x=75000192$$

Whakawehea ngā taha e rua ki te 40.

$$x=\frac{75000192}{40}$$

Whakahekea te hautanga \frac{75000192}{40} ki ōna wāhi pāpaku rawa mā te tango me te whakakore i te 8.

$$x=\frac{9375024}{5}$$