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Question Number 202297 by hardmath last updated on 24/Dec/23

$$\mathrm{If}{\mathrm{a}}^2+\mathrm{a}=5$$$$\mathrm{Find}\frac{{\mathrm{a}}^{-\mathbf{b}}+{\mathrm{a}}^{1-\mathbf{b}}+{\mathrm{a}}^{2-\mathbf{b}}}{{\mathrm{a}}^{-\mathbf{b}}}=?$$

Answered by MATHEMATICSAM last updated on 24/Dec/23

$$\frac{a^{-b}+a^{1-b}+a^{2-b}}{a^{-b}}$$$$=\frac{\cancel{a^{-b}}(1+a+a^2)}{\cancel{a^{-b}}}$$$$=a^2+a+1$$$$=5+1[\because a^2+a=5]$$$$=6$$

Answered by Rasheed.Sindhi last updated on 24/Dec/23

$$\frac{{\mathrm{a}}^{-\mathbf{b}}+{\mathrm{a}}^{1-\mathbf{b}}+{\mathrm{a}}^{2-\mathbf{b}}}{{\mathrm{a}}^{-\mathbf{b}}}$$$$=1+a+a^2=1+5=6$$

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