Răspuns:
Explicație pas cu pas:
a)
1 + 2 + 3 + ...+ 98 = 98(1 + 98)/2 = 98*99/2 = 4851
x = 4851 + 49 = 4900 = (70)^2
√x = 70
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b)
1 + 2 + 3 + .... + 49 = 49(1 +49)/2 = 49*50/2 = 1225
x = 8*1225 + 1225 = 9*1225 = 11025 = (3*35)^2
√x = 3*35 = 105
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c)
648 = 2 + (n - 1)*2 = 2 + 2n - 2 = 2n
n = 648 : 2 = 324
2 + 4 + 6 + 8 + .... + 648 = 324(2 + 648)/2 = 324*650/2 = 105300
x = 105300 - 104976 = 324 = 18^2
√x = 18
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d)
1 + 2 + 3 + 4 + .... + 224 = 224(1 + 224)/2 = 224*225/2 = 25200
x = 25200 - 7200 = 18000 = 36*5*100
√x = 60√5
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e)
450 = 2 + (n - 1)*2 = 2 + 2n - 2 = 2n
n = 450 : 2 = 225
2 + 4 + 6 + 8 + ....+ 450 = 225(2 + 450)/2 = 225*452/2 = 50850
x = 50850 - 50625 = 225 = 15^2
√x = 15
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f)
99 = 1 + (n - 1)*2 = 1 + 2n - 2 = 2n - 1
2n = 100; n = 50
1 + 3 + 5 + .....+ 99 = 50(1 + 99)/2 = 50*100/2 = 2500
x = 3*2500 - 5000 = 7500 - 5000 = 2500 = 50^2
√x = 50
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g)
100 = 2 + (n - 1)*2 = 2 + 2n - 2 = 2n
n = 100 : 2 = 50
2 + 4 + 6 + 8 + ....+ 100 = 50(2 + 100)/2 = 50*102/2 = 2550
x = 2550 = 50 = 2500 = 50^2
√x = 50
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h)
1 + 2 + 3 + .... + 120 = 120(1 + 120)/2 = 120*121/2 = 7260
x = 7260 + 484 = 7744 = 88^2
√x = 88
