Question

Разложите на множители: х^4-x^3-x+1
Вычислите:68^2-12^2/96 ^2-16^2
13^2+30*13+15^2/14*40-14*12

Answer 1

$x^{4} - x^{3} -x+1= (x^{4} - x^{3}) -x+1=x^3(x-1)-(x-1)=$$(x^3-1)(x-1)=(x-1)(x^2+x+1)(x-1)=(x-1)^2(x^2+x+1)$

$\frac{68^2-12^2}{96^2-16^2} = \frac{(68-12)(68+12)}{(96-16)(96+16)} = \frac{56*80}{70*112}$$\frac{1*8}{7*2}= \frac{8}{14} = \frac{4}{7}$

$\frac{13^2+30*13+15^2}{14*40-14*12} = \frac{13^2+2*13*15+15^2}{14*40-14*12}=\frac{(13+15)^2}{14(40-12)}$$=\frac{28^2}{14*28} = \frac{28*28}{14*28} =\frac{2*1}{1*1} =2$