Jumlah semua akar persamaan 52x+1−26⋅5x= −5 adalah ....
x = 1
x = −1
x = −1 atau x = 1
x = 5 atau x = −5
x = 5
Diketahui:
52x+1−26⋅5x= −55^{2x+1}-26\cdot5^x=\ -552x+1−26⋅5x= −5
Ditanya:
Jumlah akar-akar
Dijawab:
52x+1−26⋅5x+5=05^{2x+1}-26\cdot5^x+5=052x+1−26⋅5x+5=0
5⋅52x−26⋅5x+5=05\cdot5^{2x}-26\cdot5^x+5=05⋅52x−26⋅5x+5=0
Misalkan y = 5xy\ =\ 5^xy = 5x :
5y2−26y+5=05y^2-26y+5=05y2−26y+5=0
(5y−1)(y−5)=0\left(5y-1\right)\left(y-5\right)=0(5y−1)(y−5)=0
y = 15atau y = 5y\ =\ \frac{1}{5}atau\ y\ =\ 5y = 51atau y = 5
Substitusikan kembali nilai y:
5x = 15atau 5x = 55^x\ =\ \frac{1}{5}atau\ 5^x\ =\ 55x = 51atau 5x = 5
x = −1 atau x = 1x\ =\ -1\ atau\ x\ =\ 1x = −1 atau x = 1