Answer: [tex]x=\frac{13}{2}[/tex] is not an extraneous solution.
Step-by-step explanation: [tex](2x+3)^{\frac{3}{4} }-3=5[/tex]
Adding 3 on both the sides of the equation, we get
= [tex](2x+3)^{\frac{3}{4} }-3+3=5+3[/tex]
= [tex](2x+3)^{\frac{3}{4} }=8[/tex]
On the right hand side of the equation, 8 can also be written as
= [tex](2x+3)^{\frac{3}{4} }=(2)^{(\frac{3}{4})(4) }[/tex]
Taking power [tex]\frac{4}{3}[/tex] on both the side of the equation, we get
= [tex](2x+3)=(2)^{4}[/tex]
= [tex](2x+3)=16[/tex]
= [tex]2x=13[/tex]
= [tex]x=\frac{13}{2}[/tex]
Check for extraneous solution
Putting [tex]x=\frac{13}{2}[/tex] in the original equation [tex](2x+3)^{\frac{3}{4} }-3=5[/tex], we get
= [tex](2(\frac{13}{2}) +3)^{\frac{3}{4} }-3=5[/tex]
= [tex](16)^{\frac{3}{4} }-3=5[/tex]
= [tex]8-3=5[/tex]
= [tex]5=5[/tex]
⇒ LHS = RHS
∴ [tex]x=\frac{13}{2}[/tex] is not an extraneous solution.
Know more about Extraneous Solution: - https://brainly.com/question/4563555
