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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}<br /> 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<br /> \\a=\left(-2\right)^{26-23}+\left(-20\right)+1<br /> \\a=\left(-2\right)^{3}-20+1<br /> \\a=-8-20+1<br /> \\a =-27
iar
<br /> b=\left(1+3+5+...+9\right)-\left(2+4+6+...+10\right)+31-25<br /> \\b=\left(1+(2+1)+(4+1)+...+(8+1)\right)-2\left(1+2+3+...+5\right)+6<br /> \\b=\left(1+4\cdot 1+2\left(1+2+3+...+4\right)\right)-2\cdot\frac{5\cdot (5+1)}{2}+6<br /> \\b=\left(5+2\cdot\frac{4\cdot(4+1)}{2}\right)-5\cdot 6+6<br /> \\b=5+4\cdot 5-30+6<br /> \\b=5+20-30+6<br /> \\b=25-30+6<br /> \\b=-5+6<br /> \\b=1<br />
Calculand ax=b+53 \Rightarrow<br /> \\-27x=1+53<br /> \\-27x=54<br /> \\x=\frac{54}{-27}<br /> \\x=-2<br /> .
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.