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If $3^{(x-1)}+3^{(x+1)}=30$, then what is the value of $3^{(x+2)}+3^{x}$ ?
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The correct answer is:
90
Given: $3^{(x-1)}+3^{(x+1)}=30$
$\Rightarrow \frac{3^{\mathrm{x}}}{3}+3.3^{\mathrm{x}}=30$
Multiplying both the sides by 3 in equation (i) $3^{x}+3^{2} .3^{x}=90$
$\Rightarrow 3^{\mathrm{x}}+3^{\mathrm{x}+2}=90$
$\Rightarrow \frac{3^{\mathrm{x}}}{3}+3.3^{\mathrm{x}}=30$
Multiplying both the sides by 3 in equation (i) $3^{x}+3^{2} .3^{x}=90$
$\Rightarrow 3^{\mathrm{x}}+3^{\mathrm{x}+2}=90$
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