Tentukan himpunan penyelesaian dari persamaan berikut!

By Admin ReiPosted on October 28, 2022

$huge{} {2}^{ sqrt{100 {x}^{2} } : + : 2y} = 32 \ huge{} {5}^{ sqrt{ sqrt{256 {x}^{4} } } : - : 2y } = 125$

Tentukan himpunan penyelesaian dari persamaan berikut!

Jawaban:

{4/7, -5/14}

Penjelasan dengan langkah–langkah:

${2}^{ sqrt{100 {x}^{2} } + 2y } = 32 \ {2}^{10x + 2y} = {2}^{5} \ 10x + 2y = 5$

Lanjut persamaan kedua:

${5}^{ sqrt{ sqrt{256 {x}^{4} } } - 2y} = 125 \ {5}^{4x - 2y} = {5}^{3} \ 4x - 2y = 3$

10x+2y=5

4x-2y= 3

————- +

14x= 8

x= 8/14= 4/7

10(4/7)+2y=5

40/7+2y=5

2y= 5-40/7

2y= 35/7-40/7

2y= -5/7

y= -5/14

❐ Eksponen

$rm x to dfrac {4}{7}$

$rm y to -dfrac {5}{14}$

_____________________________

Persamaan (i)

$rm 2^{sqrt {100x²} + 2y} = 32$

$rm 2^{sqrt {100x²} + 2y} = 2⁵$

$rm sqrt {100x²} + 2y = 5$

$rm sqrt {10²} sqrt {x²} + 2y = 5$

$rm 10x + 2y = 5$

Persamaan (ii)

$rm 5^{sqrt {sqrt {256x⁴}} - 2y} = 125$

$rm 5^{sqrt {sqrt {256x⁴}} - 2y} = 5³$

$rm sqrt {sqrt {256x⁴}} - 2y = 3$

$rm 256^{frac {1}{4}} ~x⁴{frac {1}{4}} - 2y = 3$

$rm 4⁴^{frac {1}{4}} ~x - 2y = 3$

$rm 4x - 2y = 3$

$rm 2y = 4x - 3$

Substitusikan

$rm 10x + 2y = 5$

$rm 10x + (4x - 3) = 5$

$rm 14x = 8$

$rm x = dfrac {8}{14}$

$rm x = dfrac {4}{7}$

Substitusikan

$rm 2y = 4x - 3$

$rm 2y = 4 ~.~dfrac {4}{7} - 3$

$rm 2y = -dfrac {5}{7}$

$rm y = -dfrac {5}{14}$