Exercitii operatii cu numere intregi

Astazi o sa rezolvam cat mai multe exercitii in care apar numerele intregi, adica operatii cu numere intregi:
1) Rezolvati ecuatia $ax=b+53$ pentru:

$a=\left[\left(-3\right)^{13}\right]^{2}:\left(-2\right)^{23}+\left(-5\right)\cdot\left(-2\right)^{2}+\left(-1\right)^{2010} b=\left(1-2+3-4+5-6+...+9-10\right)+\left(+31\right)-\left(-5\right)^{2}$
Calculam mai intai a si b, iar apoi ecuatia. Incepem prin a calcula a
$a=\left(-2\right)^{26}:\left(-2\right)^{23}+\left(-5\right)\cdot 4+1 \\a=\left(-2\right)^{26-23}+\left(-20\right)+1 \\a=\left(-2\right)^{3}-20+1 \\a=-8-20+1 \\a =-27$
iar
$ b=\left(1+3+5+...+9\right)-\left(2+4+6+...+10\right)+31-25 \\b=\left(1+(2+1)+(4+1)+...+(8+1)\right)-2\left(1+2+3+...+5\right)+6 \\b=\left(1+4\cdot 1+2\left(1+2+3+...+4\right)\right)-2\cdot\frac{5\cdot (5+1)}{2}+6 \\b=\left(5+2\cdot\frac{4\cdot(4+1)}{2}\right)-5\cdot 6+6 \\b=5+4\cdot 5-30+6 \\b=5+20-30+6 \\b=25-30+6 \\b=-5+6 \\b=1 $
Calculand $ax=b+53 \Rightarrow \\-27x=1+53 \\-27x=54 \\x=\frac{54}{-27} \\x=-2 $ .
Deci am gasit solutia ecuatiei in care am efectuat operatii cu numere intregi.In curand si alte exercitii explicate cu operatii cu numere intregi vor fi postate pe site-ul Mate Pedia.

Exercitii operatii cu numere intregi

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