Дано:a1=-8
a2=-1
a3=6
Найти:a51
Решение:
an=a1+d(n-1)
d=a2-a1=-1-(-8)=-1+8=7
a51=a1+d(51-1)=-8+7(51-1)=-8+7*50=-8+350=342
Ответ:342
1) ![(m-n)(m+3)=m\cdot m+3\cdot m-m\cdot n-3\cdot n=m^{2}+3m-mn-3n](https://tex.z-dn.net/?f=%28m-n%29%28m%2B3%29%3Dm%5Ccdot%20m%2B3%5Ccdot%20m-m%5Ccdot%20n-3%5Ccdot%20n%3Dm%5E%7B2%7D%2B3m-mn-3n)
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2) ![(4+5a)(5a-4)=4\cdot5a-4\cdot4+5a\cdot5a-4\cdot5a=20a-16+25a^{2}-20a=25a^{2}+(20a-20a)-16=25a^{2}-16](https://tex.z-dn.net/?f=%284%2B5a%29%285a-4%29%3D4%5Ccdot5a-4%5Ccdot4%2B5a%5Ccdot5a-4%5Ccdot5a%3D20a-16%2B25a%5E%7B2%7D-20a%3D25a%5E%7B2%7D%2B%2820a-20a%29-16%3D25a%5E%7B2%7D-16)
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3) ![(8b+5a)(5a-8b)=5a\cdot8b-8b\cdot8b+5a\cdot5a-5a\cdot8b=40ab-64b^{2}+25a^{2}-40ab= 25a^{2}+(40ab-40ab)-64b^{2}=25a^{2}-64b^{2}](https://tex.z-dn.net/?f=%288b%2B5a%29%285a-8b%29%3D5a%5Ccdot8b-8b%5Ccdot8b%2B5a%5Ccdot5a-5a%5Ccdot8b%3D40ab-64b%5E%7B2%7D%2B25a%5E%7B2%7D-40ab%3D%2025a%5E%7B2%7D%2B%2840ab-40ab%29-64b%5E%7B2%7D%3D25a%5E%7B2%7D-64b%5E%7B2%7D)
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4) ![(c-7)(c+7)=c\cdot c+7\cdot c-7\cdot c-7\cdot7=c^{2}+7c-7c-49=c^{2}+(7c-7c)-49=c^{2}-49](https://tex.z-dn.net/?f=%28c-7%29%28c%2B7%29%3Dc%5Ccdot%20c%2B7%5Ccdot%20c-7%5Ccdot%20c-7%5Ccdot7%3Dc%5E%7B2%7D%2B7c-7c-49%3Dc%5E%7B2%7D%2B%287c-7c%29-49%3Dc%5E%7B2%7D-49)
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5) ![(7x-2)(7x+2)=7x\cdot7x+2\cdot7x-2\cdot7x-2\cdot2=49x^{2}+14x-14x-4=49x^{2}+(14x-14x)-4= 49x^{2}-4](https://tex.z-dn.net/?f=%287x-2%29%287x%2B2%29%3D7x%5Ccdot7x%2B2%5Ccdot7x-2%5Ccdot7x-2%5Ccdot2%3D49x%5E%7B2%7D%2B14x-14x-4%3D49x%5E%7B2%7D%2B%2814x-14x%29-4%3D%2049x%5E%7B2%7D-4)
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6) ![(10p-6q)(10p+6q)=10p\cdot10p+10p\cdot6q-10p\cdot6q-6q\cdot6q=100p^{2}+60pq-60pq-36q^{2}=100p^{2}+(60pq-60pq)-36q^{2}=100p^{2}-36q^{2}](https://tex.z-dn.net/?f=%2810p-6q%29%2810p%2B6q%29%3D10p%5Ccdot10p%2B10p%5Ccdot6q-10p%5Ccdot6q-6q%5Ccdot6q%3D100p%5E%7B2%7D%2B60pq-60pq-36q%5E%7B2%7D%3D100p%5E%7B2%7D%2B%2860pq-60pq%29-36q%5E%7B2%7D%3D100p%5E%7B2%7D-36q%5E%7B2%7D)
-x²-5x+14=0
x²+5x-14=0
a=1 b=5 c=-14
D=b²-4ac
D=25-4*1*(-14)=25+56=81>0 значит 2 корня
x12=
![\frac{-5+-9}{2} ](https://tex.z-dn.net/?f=%20%5Cfrac%7B-5%2B-9%7D%7B2%7D%0A%20)
x1=-7
x2=2
Ответ: -7;2
Y-2x=8
2x+3y=6
4y=14
y=14:4
y=3.5
2x+3×3.5=6
2x=-4.5
x=-2.25
Ответ: (-2.25 ; 3.5)
А/3=х(ост1) а=3х+1
в/3=у(ост2) в=3у+2
доказать
а*в/3=z(ост2)
(9ху+3х+3у+2)/3=ост2