Ответы
Ответ::To solve the inequality х2+6х-40 >0, we can use the following steps:
Factor the quadratic expression х2+6х-40:
х2+6х-40 = (x-4)(x+10)
Find the zeros of the expression (i.e., the values of x that make the expression equal to zero):
(x-4)(x+10) = 0
x-4 = 0 or x+10 = 0
x = 4 or x = -10
Use these zeros to divide the real number line into three intervals:
Interval 1: x < -10
Interval 2: -10 < x < 4
Interval 3: x > 4
Test a value in each interval to determine the sign of the expression in that interval:
Interval 1: Test x = -11
х2+6х-40 = (-11-4)(-11+10) = (-15)(-1) = 15 > 0
The expression is positive in this interval.
Interval 2: Test x = 0
х2+6х-40 = (0-4)(0+10) = (-4)(10) = -40 < 0
The expression is negative in this interval.
Interval 3: Test x = 5
х2+6х-40 = (5-4)(5+10) = (1)(15) = 15 > 0
The expression is positive in this interval.
Write the solution as the union of the intervals where the expression is positive:
х2+6х-40 >0 for x < -10 or x > 4.
Therefore, the solution to the inequality х2+6х-40 >0 is x < -10 or x > 4.
Объяснение
Ответ:
×>5
Объяснение:
×+2+6×-40>0
2x+6×-40>0
8x-40 > 0
8x> 40
×>5
XE (5, +00) , {x|×> 5}