Answer:
A). [tex]x=\sqrt{8i}[/tex]
B). [tex]x=2i[/tex]
Step-by-step explanation:
Part A
[tex]5+x^{2} =2*x^{2} +13\\5-5+x^{2}-2*x^{2} =2*x^{2} -2*x^{2}+13-5 \\x^{2}-2*x^{2}=13-5\\-x^{2}=8\\x^{2}=-8\\x=\sqrt{8i}[/tex]
Check:
[tex]5+(\sqrt{8i})^{2}=2*(\sqrt{8i})^{2}+13[/tex]
[tex]5+8i^{2}=2*8i^{2}+13\\5+8(-1)=2*8(-1)+13\\5-8=-16+13\\-3=-3[/tex]
Part B
[tex]5+x^{3}=2*x^{3}+13\\5-5+x^{3}=2*x^{3}-2*x^{3}+13-5\\x^{3}-2*x^{3}=13-5\\-x^{3}=8\\x^{3}=-8\\x=-8^{\frac{1}{3} } \\x=8i^{\frac{1}{3} }\\x=2i[/tex]
Check:
[tex]5+(2i)^{3}=2*(2i)^{3}+13\\5+8i^{3}=2*8i^{3}+13\\5+8-i=16-i+13\\5-8i=-16i+13\\5-13-8i+8i=-16i+8i+13-13\\-8=-8i\\-8=-8[/tex]