+0  
 
0
138
2
avatar

\sqrt(x^(2)-13x+12)<=5-x

 Dec 24, 2019
 #1
avatar
0

Hints:

-Square both sides

-Solve the equation for x

-Remember when dividing by - or multiplying by - we multiply both sides and in inequalities, we switch the sign e.g, if it is < then it will be > if being multiplied or divided by -) 

-If real numbers find intervals 

 Dec 24, 2019
 #2
avatar+111360 
+1

√ [x^2 - 13x + 12]  ≤  5 - x   square both sides

 

x^2  - 13x + 12  ≤   x^2  - 10x  +  25       simplify

 

-3x ≤ 13       divide both sides by   -3, reverse the inequality sign 

 

x ≥ - 13/3

 

But   we also   must have that

 

x^2 - 13x + 12  ≥ 0

 

(x - 12) ( x - 1) ≥ 0

 

The solutions to this are

 

(-inf, 1 ]  U  [12, inf)

 

We must take the  most restrictive interval....this is

 

-13/3 ≤ x ≤ 1

 

 

cool cool cool

 Dec 24, 2019

21 Online Users

avatar
avatar
avatar
avatar
avatar
avatar