Question

Sa se rezolve in R inecuatiile:

a) $\sqrt{2-x} \leq x$

b)$\sqrt{ x^{2} -55x+250}<x-14$

c)$\sqrt{ x^{2} -3x+2}>2-x$

Answer 1

a)(2-x)≤x²
-x²-x+2≤0       (-1)
x²+x-2≥0
Δ=1+8
x1=(-1+3)/2=2/2=1
x2=(-1-3)/2=-4/2=-2
x∈(-α, -2]u[1,+α)
b)x²-55x+250<(x-14)²
x²-55x+250<x²-28x+196
x²-x²-55x+28x+250-196<0
-27x+54<0
-27x<-54    (-1)
x>54/27
x>2,25
x∈(2,25,+α)
c)
x²-3x+2>(2-x)²
x²-3x+2>4-4x+x²
x²-x²-3x+4x+2-4>0
x-2>0
x>2
X∈(2,+α)