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Question Number 171070 by MathsFan last updated on 07/Jun/22

$${\mathbf{x}}^2-1=2^{\mathbf{x}}$$$$\mathbf{find}\mathbf{x}$$

Answered by Rasheed.Sindhi last updated on 07/Jun/22

$${\mathrm{x}}^2-1=2^{\mathrm{x}};\mathrm{find}\mathrm{x}$$$$Assuming\mathrm{x}\mathrm{a}\mathrm{whole}\mathrm{number}:$$$$(\mathrm{x}-1)(\mathrm{x}+1)=2^{\mathrm{x}}$$$$\mathrm{Both}\mathrm{x}-1\mathrm{\&}\mathrm{x}+1\mathrm{are}\mathrm{powers}\mathrm{of}2$$$$\mathrm{and}\mathrm{have}\mathrm{difference}2\mathrm{between}\mathrm{them}.$$$$\mathrm{Only}2\mathrm{\&}4\mathrm{are}\mathrm{such}\mathrm{numbers}$$$$\mathrm{x}-1=2\wedge \mathrm{x}+1=4\Rightarrow \mathrm{x}=3$$$$3^2-1=2^3✓$$$$\mathrm{x}=3$$

Commented by MathsFan last updated on 07/Jun/22

$$thanksalot:)$$

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