If z2+1/z2=34 fund the value is z3+1/z3 using only the positive value of z+1/z
Answers
» Given:
» To find:
» We know that,
» Solution -
Finding value of
Finding value of
Answer:
» Given:
z^2+\frac{1}{z^2} = 34z
2
+
z
2
1
=34
» To find:
the\:value\:of\:z^3+\frac{1}{z^3}thevalueofz
3
+
z
3
1
» We know that,
\begin{gathered} (a+b)^2 = a^2+b^2+2ab\\ \\ \\ (a+b)^3 = a^3+b^3+3ab(a+b)\end{gathered}
(a+b)
2
=a
2
+b
2
+2ab
(a+b)
3
=a
3
+b
3
+3ab(a+b)
» Solution -
Finding value of z+\frac{1}{z}z+
z
1
\begin{gathered} (a+b)^2 = a^2+b^2+2ab\\ \\ \\ by\: putting\:values\\ \\ \\ (z+\frac{1}{z})^2 = z^2+\frac{1}{z^2} +2(z\times\frac{1}{z}) \\ \\ \\ (z+\frac{1}{z})^2 = 34+2\\ \\ \\(z+\frac{1}{z})^2 = 36\\ \\ \\z+\frac{1}{z} = \sqrt{36}\\ \\ \\{\pink{\boxed{z+\frac{1}{z} = 6}}}\end{gathered}
(a+b)
2
=a
2
+b
2
+2ab
byputtingvalues
(z+
z
1
)
2
=z
2
+
z
2
1
+2(z×
z
1
)
(z+
z
1
)
2
=34+2
(z+
z
1
)
2
=36
z+
z
1
=
36
z+
z
1
=6
Finding value of z^3+\frac{1}{z^3}z
3
+
z
3
1
\begin{gathered}(a+b)^3 = a^3+b^3+3ab(a+b)\\ \\ \\ by\: putting\:values\\ \\ \\ (z+\frac{1}{z})^3 = z^3+\frac{1}{z^3}+3(z\times\frac{1}{z})(z+\frac{1}{z})\\ \\ \\ (6)^3 = z^3+\frac{1}{z^3}+3(6)\\ \\ \\ 216 = z^3+\frac{1}{z^3}+18\\ \\ \\ z^3+\frac{1}{z^3} = 216-18 \\ \\ \\ {\purple{\boxed{z^3+\frac{1}{z^3} = 198}}}\end{gathered}
(a+b)
3
=a
3
+b
3
+3ab(a+b)
byputtingvalues
(z+
z
1
)
3
=z
3
+
z
3
1
+3(z×
z
1
)(z+
z
1
)
(6)
3
=z
3
+
z
3
1
+3(6)
216=z
3
+
z
3
1
+18
z
3
+
z
3
1
=216−18
z
3
+
z
3
1
=198