Question

x²+1010=2+4+6+8+...+2016+2018+2020​

Answer 1

Răspuns:

${x}^{2} + 1010 = 2 + 4 + 6 + ... + 2016 + 2018 + 2020 \\ {x}^{2} + 1010 = 2 \times (1 + 2 + 3 + ... + 1008 + 1009 + 1010) \\ {x}^{2} + 1010 = 2 \times \frac{1010 \times 1011}{2} \\ {x}^{2} + 1010 = 1010 \times 1011 \\ {x}^{2} = 1010 \times 1011 - 1010 \\ {x}^{2} = 1010 \times (1011 - 1) \\ {x}^{2} = 1010 \times 1010 = {1010}^{2} \\ x = \sqrt{1010 {}^{2} } = |1010| \\ x = 1010 \: sau \: x = - 1010$

Answer 2

Răspuns:

Explicatie pas cu pas:

x²+1010=2+4+6+8+...+2016+2018+2020​

x²+1010=2(1+2+3+4+.....+1010)     aplicam Suma Gauss

x²+1010 =2·1010·1011/2

x²=1010·1011-1010=1010(1011-1)=1010·1010=1010²

x=1010