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A simple inequality (Posted on 2014-12-31) Difficulty: 2 of 5
Given:
x>0, y>0, x+y=1

Prove that
(1 + 1/x)(1 + 1/y) ≥ 9.

No Solution Yet Submitted by Ady TZIDON    
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Some Thoughts no proof--just demonstration | Comment 1 of 4
 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



  Posted by Charlie on 2014-12-31 11:08:03
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