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Aflați x stiind ca: a) x×(1+2+3+...+100)=60.000

b) (1+2+3+...+100):x=101


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Răspuns :

[tex]a)x(1 + 2 + 3 + ... + 100) = 60000[/tex]

[tex]x \times \frac{100(100 + 1)}{2} = 60000[/tex]

[tex]x \times \frac{100 \times 101}{2} = 60000[/tex]

[tex]x \times 50 \times 101 = 60000 \: | \div 50[/tex]

[tex]101x = 1200[/tex]

[tex]x = \frac{1200}{101} [/tex]

[tex]b)(1 + 2 + 3 + ... + 100) \div x = 101[/tex]

[tex] \frac{100(100 + 1)}{2} \div x = 101[/tex]

[tex] \frac{100 \times 101}{2} \div x = 101[/tex]

[tex] \frac{50 \times 101}{x} = 101 \: | \times x[/tex]

[tex]101x = 50 \times 101 \: | \div 101[/tex]

[tex]x = 50[/tex]