Given:
x>0, y>0, x+y=1
Prove that
(1 + 1/x)(1 + 1/y) ≥ 9.
x (1+1/x)(1+1/(1-x))
0.01 203.0202020
0.02 103.0408163
0.03 69.7285223
0.04 53.0833333
0.05 43.1052632
0.06 36.4609929
0.07 31.7219662
0.08 28.1739130
0.09 25.4200244
0.10 23.2222222
0.11 21.4290092
0.12 19.9393939
0.13 18.6834660
0.14 17.6112957
0.15 16.6862745
0.16 15.8809524
0.17 15.1743444
0.18 14.5501355
0.19 13.9954516
0.20 13.5000000
0.21 13.0554551
0.22 12.6550117
0.23 12.2930548
0.24 11.9649123
0.25 11.6666667
0.26 11.3950104
0.27 11.1471334
0.28 10.9206349
0.29 10.7134531
0.30 10.5238095
0.31 10.3501636
0.32 10.1911765
0.33 10.0456807
0.34 9.9126560
0.35 9.7912088
0.36 9.6805556
0.37 9.5800086
0.38 9.4889643
0.39 9.4068937
0.40 9.3333333
0.41 9.2678793
0.42 9.2101806
0.43 9.1599347
0.44 9.1168831
0.45 9.0808081
0.46 9.0515298
0.47 9.0289041
0.48 9.0128205
0.49 9.0032013
0.50 9.0000000
0.51 9.0032013
0.52 9.0128205
0.53 9.0289041
0.54 9.0515298
0.55 9.0808081
0.56 9.1168831
0.57 9.1599347
0.58 9.2101806
0.59 9.2678793
0.60 9.3333333
0.61 9.4068937
0.62 9.4889643
0.63 9.5800086
0.64 9.6805556
0.65 9.7912088
0.66 9.9126560
0.67 10.0456807
0.68 10.1911765
0.69 10.3501636
0.70 10.5238095
0.71 10.7134531
0.72 10.9206349
0.73 11.1471334
0.74 11.3950104
0.75 11.6666667
0.76 11.9649123
0.77 12.2930548
0.78 12.6550117
0.79 13.0554551
0.80 13.5000000
0.81 13.9954516
0.82 14.5501355
0.83 15.1743444
0.84 15.8809524
0.85 16.6862745
0.86 17.6112957
0.87 18.6834660
0.88 19.9393939
0.89 21.4290092
0.90 23.2222222
0.91 25.4200244
0.92 28.1739130
0.93 31.7219662
0.94 36.4609929
0.95 43.1052632
0.96 53.0833333
0.97 69.7285223
0.98 103.0408163
DefDbl A-Z
Dim crlf$
Function mform$(x, t$)
a$ = Format$(x, t$)
If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
mform$ = a$
End Function
Private Sub Form_Load()
ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents
For x = 0.01 To 0.99 Step 0.01
y = 1 - x
Text1.Text = Text1.Text & mform(x, "0.00") & mform((1 + 1 / x) * (1 + 1 / y), "###0.0000000") & crlf
Next
Text1.Text = Text1.Text & " done"
End Sub
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Posted by Charlie
on 2014-12-31 11:08:03 |
no proof--just demonstration
