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Question Number 208034 by ali009 last updated on 02/Jun/24

Commented by ali009 last updated on 02/Jun/24

$$howthatcanbeproved?$$

Answered by Frix last updated on 02/Jun/24

$$s^2+\frac{s}{2}+2={(s+\frac{1}{4})}^2+\frac{31}{16}={(s+\frac{1}{4})}^2+{\left(\frac{\sqrt{31}}{4}\right)}^2$$$$\frac{\sqrt{31}}{4}\ne 1.39$$$${(s+.25)}^2+1.{39}^2=s^2+.5s+1.9946$$$$1.9946\ne 2$$$$\mathrm{So}\mathrm{there}\mathrm{is}\mathrm{no}\mathrm{proof}.$$

Commented by ali009 last updated on 02/Jun/24

$$ithink{it}^{\prime }s$$$$\sqrt{2-0.0625}\simeq 1.39$$$$because$$$${(s+0.25)}^2+{\left(\sqrt{2-0.0625}\right)}^2=s^2+\frac{s}{2}+2$$

Commented by Frix last updated on 03/Jun/24

$$\mathrm{Mathematical}\mathrm{proofs}\mathrm{are}\mathrm{precise}.\mathrm{You}\mathrm{can}$$$$\mathrm{round}\mathrm{numbers}\mathrm{but}\mathrm{you}\mathrm{cannot}\mathrm{prove}\mathrm{that}$$$$2=1.9946\mathrm{or}\frac{\sqrt{31}}{4}=1.39$$

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