Question

VA ROGGGGG DAU COROANAAAA
rasp doar daca stiti va rog
pb 16

Answer 1

Explicație pas cu pas:

a)

x < 0 => |x| = - x

x < 0 <=> -x > 0 <=> 1 - x > 1

=> |1 - x| = 1 - x

$|x| + 2x + 1 + |1 - x| =$

$= - x + 2x + 1 + 1 - x = 2x - 2x + 2 = \bf 2$

b)

x² + 1 > 0 => |x² + 1| = x² + 1

x < 5 => x - 5 < 0 => |x - 5| = 5 - x

x > 0 => √x⁴ = |x²| = x² > 0

$|{x}^{2} + 1| + 5|x - 5| + 5x - 16 - \sqrt{x^{4}}=$

$= {x}^{2} + 1 + 5(5 - x) + 5x - 16 - {x}^{2} = \\ = {x}^{2} + 1 + 25 - 5x + 5x - 16 - {x}^{2} \\ = {x}^{2} - {x}^{2} + 5x - 5x + 26 - 16 = \bf 10$

c)

-3 < x => x + 3 > 0 => |x + 3| = x + 3

x < 1 => x - 1 < 0 => |x - 1| = 1 - x

x < 1 => x - 2 < 1 - 2 <=> x - 2 < -1 < 0

2x - 4 = 2(x - 2) => |2x - 4| = 4 - 2x

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

$= - (x + 3) + |x - 1| - (4 - 2x)$

$= - x - 3 + 1 - x - 4 + 2x$

$= 2x - 2x + 1 - 7 = \bf - 6$