Question

Tìm\(x\in Z\)thỏa mãn (x² - 1)(x² - 4)(x² - 7)(x² - 10) < 0

Answer 1

lập bảng cho nành v10; v7\(=\sqrt{10};\sqrt{7}\)

x	-vc	-v10		-v7		-2		-1	0	1		2		v7		v10	+vc
x+v10	-	0	+	+	+	+	+	+	+	+	+	+	+	+	+	+	+
x+v7	-	-	-	0	+	+	+	+	+	+	+	+	+	+	+	+	+
x+2	-	-	-	-	-	0	+	+	+	+	+	+	+	+	+	+	+
x+1	-	-		-	--		-	0	+	+	+	+	+	+	+	+	+
x-1	-	-			-				-	0	+
x-2	-	-			-						-	0	+
x-v7	-	-			-						-		-	0	+
x-v10	-	-			-						-		-		-	0	+
VT	+	0	-	0	+	0	-	0	+	0	-	0	+	0	-	0	+

các khoảng x thỏa man la

-v10<x<-v7

-1<x<-2

1<x<2

v7<x<v10

x nguyen

=> x={-3,3}

Answer 2

https://olm.vn/hoi-dap/tim-kiem?q=Ch%E1%BB%A9ng+minh+r%E1%BA%B1ng:++(x2-1).(x2-4).(x2-7).(x2-10)%3C0&id=153167