Kelkel03
Kelkel03 Kelkel03
  • 17-04-2017
  • Mathematics
contestada

It is an odd two digit number
The sum of its digits is 8
The sum of the squares of its digits is 50

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Halfblood94
Halfblood94 Halfblood94
  • 17-04-2017
Could be either 17 or 71. The square of 7 is 49, square of 1 is 1. 49+1=50
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shockwave89
shockwave89 shockwave89
  • 17-04-2017
⇔ Consider the first digit = a, and the second digit = b

≡ We know that:
⇔ [tex](a+b)=8[/tex]
⇔ [tex]a^{2}+b^{2}=50[/tex]

≡ Solution:
⇒ [tex]a^{2}+b^{2}=(a+b)^{2}-2ab[/tex]
⇒ [tex]50=(8)^{2}-2ab[/tex]
⇒ [tex]2ab=64-50[/tex]
⇒ [tex]2ab=14[/tex]
⇒ [tex](a).(b)=7[/tex]

⇔ Cause a × b = 7, there are 2 option the value of ab that:
∴ a = 1, b = 7 → 17
∴ a = 7, b = 1 → 71
Ver imagen shockwave89
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