Himpunan penyelesaian dari persamaan adalah ....

Pertanyaan

Himpunan penyelesaian dari persamaan $open parentheses 3 straight x minus 2 close parentheses to the power of straight x squared minus 3 straight x plus 2 end exponent equals open parentheses straight x plus 4 close parentheses to the power of straight x squared minus 3 straight x plus 2 end exponent$ adalah ....

{3}
{1,2}
{1,3}
{1,2,3}
{0,1,2,3}

Pembahasan Soal:

$left parenthesis 3 straight x minus 2 right parenthesis to the power of straight x squared minus 3 straight x plus 2 end exponent equals left parenthesis straight x plus 4 right parenthesis to the power of straight x squared minus 3 straight x plus 2 end exponent rightwards arrow straight f left parenthesis straight x right parenthesis to the power of straight g left parenthesis straight x right parenthesis end exponent equals straight h left parenthesis straight x right parenthesis to the power of straight g left parenthesis straight x right parenthesis end exponent rightwards double arrow straight f left parenthesis straight x right parenthesis equals straight h left parenthesis straight x right parenthesis space space space space 3 straight x space minus space 2 equals straight x space plus space 4 space space space space space space space space space space space space 2 straight x equals 6 left right double arrow straight x equals 3 rightwards double arrow straight g left parenthesis straight x right parenthesis equals 0 space dengan space syarat space straight f left parenthesis straight x right parenthesis not equal to 0 space dan space straight h left parenthesis straight x right parenthesis not equal to 0 space space space space space straight x squared minus 3 straight x space plus 2 space equals 0 space space space space space left parenthesis straight x minus 1 right parenthesis left parenthesis straight x minus 2 right parenthesis equals 0 space space space space space straight x equals 1 space atau space straight x equals 2$

Untuk x=1 diperoleh

$space space space space space straight f left parenthesis 1 right parenthesis equals 3 left parenthesis 1 right parenthesis minus 2 equals 1 not equal to 0 space space space space space straight h left parenthesis 1 right parenthesis equals 1 plus 4 equals 5 not equal to 0$

Untuk x=2 diperoleh

$space space space space space straight f left parenthesis 2 right parenthesis equals 3 left parenthesis 2 right parenthesis minus 2 equals 4 not equal to 0 space space space space space straight h left parenthesis 2 right parenthesis equals 2 plus 4 equals 6 not equal to 0$

Himpunan penyelesaian {1,2,3}

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 22 Desember 2020

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