Question

помогите срочно выделите квадраты двучлена из квадратов трехчлена:1)х²+6х-18；2)х²+8х-11；3)х²+5х-8；4)х²+7х-1；5)-х²+7х-12；6)-х²+8х+8​

Answer 1

$x^2+6x-18=(x+3)^2-9-18=(x+3)^2-27\\\\\\x^2+8x-11=(x+4)^2-16-11=(x+4)^2-27\\\\\\x^2+5x-8=(x+\frac{5}{2})^2-\frac{25}{4}-8=(x+\frac{5}{2})^2-\frac{57}{4}=(x+2,5)^2-14,25\\\\\\x^2+7x-1=(x+\frac{7}{2})^2-\frac{49}{4}-1=(x+\frac{7}{2})^2-\frac{53}{4}=(x+3,5)^2-13,25\\\\\\-x^2+7x-12=-(x^2-7x+12)=-\Big ((x-\frac{7}{2})^2-\frac{49}{4}+12\Big )=\\=-\Big ((x-\frac{7}{2})^2-\frac{1}{4}\Big )=\frac{1}{4}-(x-\frac{7}{2})^2=0,25-(x-3,5)^2\\\\\\-x^2+8x+8=-(x^2-8x-8)=-\Big ((x-4)^2-16-8\Big )=\\=-\Big ((x-4)^2-24\Big )=24-(x-4)^2$

$P.S.\; \; \; x^2\pm px+q=(x\pm \frac{p}{2})^2-(\frac{p}{2})^2+q$