How do you solve sqrt(3x^2-11)=x+1 and identify any restrictions?
1 Answer
Mar 29, 2018
Explanation:
color(blue)"square both sides"
rArr(sqrt(3x^2-11))^2=(x+1)^2
rArr3x^2-11=x^2+2x+1
rArr2x^2-2x-12=0larrcolor(blue)"in standard form"
rArr2(x^2-x-6)=0
rArr2(x-3)(x+2)=0
"equate each factor to zero and solve for x"
x-3=0rArrx=3
x+2=0rArrx=-2
color(blue)"As a check" Substitute these values into the equation and if both sides are equal then they are the solutions.
sqrt(27-11)=sqrt16=4" and "3+1=4
sqrt(12-11)=1" and "-2+1=-1
"the solution is "x=3
x=-2" is an extraneous solution"
