Solve the equations in Parts A and B using inverse operations. Check your solutions. In your final answer, include all of your work. Part A: 5+x^2= 2x^2 + 13 Part B: 5+x^3=2x^3+13
Answers
Answer:
A). x=\sqrt{8i}x=
8i
B). x=2ix=2i
Step-by-step explanation:
Part A
\begin{gathered}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}\end{gathered}
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=
8i
Check:
5+(\sqrt{8i})^{2}=2*(\sqrt{8i})^{2}+135+(
8i
)
2
=2∗(
8i
)
2
+13
\begin{gathered}5+8i^{2}=2*8i^{2}+13\\5+8(-1)=2*8(-1)+13\\5-8=-16+13\\-3=-3\end{gathered}
5+8i
2
=2∗8i
2
+13
5+8(−1)=2∗8(−1)+13
5−8=−16+13
−3=−3
Part B
\begin{gathered}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\end{gathered}
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
3
1
x=8i
3
1
x=2i
Check:
\begin{gathered}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\end{gathered}
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
Step-by-step explanation:
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Answer:
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Step-by-step explanation: