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МатематикаГДЗ по алгебре 7 класс Макарычев ФГОС Задание 1224
Задание 1224
\[\boxed{\text{1224.}\text{\ }еуроки - ответы\ на\ пятёрку}\]
\[\textbf{а)}\ x^{8} + x^{4} - 2 = x^{8} + x^{4} - 1 -\]
\[- 1 = \left( x^{8} - 1 \right) + \left( x^{4} - 1 \right) =\]
\[= \left( x^{4} - 1 \right)\left( x^{4} + 1 \right) +\]
\[+ \left( x^{2} - 1 \right)\left( x^{2} + 1 \right) =\]
\[= \left( x^{2} - 1 \right)\left( x^{2} + 1 \right){(x}^{4} + 1) +\]
\[+ (x - 1)(x + 1)\left( x^{2} + 1 \right) =\]
\[= (x - 1)(x + 1)\left( x^{2} + 1 \right)\]
\[\left( x^{4} + 1 \right) + (x - 1)(x + 1)\]
\[\left( x^{2} + 1 \right) =\]
\[= (x - 1)(x + 1)\left( x^{2} + 1 \right)\]
\[\left( x^{4} + 1 + 1 \right) = (x - 1)(x + 1)\]
\[\left( x^{2} + 1 \right)\left( x^{4} + 2 \right)\]
\[\textbf{б)}\ a^{5} - a^{2} - a - 1 = \left( a^{5} - a \right) -\]
\[- \left( a^{2} + 1 \right) = a\left( a^{4} - 1 \right) -\]
\[- \left( a^{2} + 1 \right) =\]
\[= a\left( a^{2} - 1 \right)\left( a^{2} + 1 \right) -\]
\[- \left( a^{2} + 1 \right) = \left( a^{2} + 1 \right)\]
\[\left( a\left( a^{2} - 1 \right) - 1 \right) =\]
\[= \left( a^{2} + 1 \right)\left( a^{3} - a - 1 \right)\]
\[\textbf{в)}\ n^{4} + 4 = n^{4} + 4 - 4n^{2} +\]
\[+ 4n^{2} = \left( n^{4} + 4n^{2} + 4 \right) -\]
\[- 4n^{2} =\]
\[= \left( n^{2} + 2 \right)^{2} - (2n)^{2} =\]
\[= (n^{2} + 2 - 2n)(n^{2} + 2 + 2n)\]
\[\textbf{г)}\ n^{4} + n^{2} + 1 = n^{4} + n^{2} + 1 +\]
\[+ n^{2} - n^{2} = \left( n^{4} + 2n^{2} + 1 \right) -\]
\[- n^{2} =\]
\[= \left( n^{2} + 1 \right)^{2} - n^{2} =\]
\[= \left( n^{2} + 1 - n \right)(n^{2} + 1 + n)\]
