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Answers
★FIND:
★GIVEN,
★SOLUTION:
Here,
Answer:
★FIND:
x {}^{4} - \frac{1}{x {}^{4} } = ?x
4
−
x
4
1
=?
★GIVEN,
\begin{lgathered}x = 3 + 2 \sqrt{3} \\ x {}^{4} - \frac{1}{x {}^{4} } = ?\end{lgathered}
x=3+2
3
x
4
−
x
4
1
=?
★SOLUTION:
Here,
x = 3 + 2 \sqrt{3} \: and \: \frac{1}{x} = 3 - 2 \sqrt{3}x=3+2
3
and
x
1
=3−2
3
\begin{lgathered}= > (x + \frac{1}{x} ) {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } + 2(x)( \frac{1}{x} ) \\ = > (3 + 2 \sqrt{3} + (3 - 2 \sqrt{3} )) {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } + 2 \\ = > (3 + 2 \sqrt{3} + 3 - 2 \sqrt{3} ) {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } + 2 \\ = >(3 + 3) {}^{2} = x { }^{2} + \frac{1}{x {}^{2} } + 2 \\ = > (6) {}^{2} = x {}^{2} + \frac{1}{x {}^{2} } + 2 \\ = > 36 - 2 = x {}^{2} + \frac{1}{x {}^{2} } \\ = > 34 = x {}^{2} + \frac{1}{x {}^{2} } \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: s.o.b.s \\ = > (34) {}^{2} = (x {}^{2} + \frac{1}{x {}^{2} } ) {}^{2} \\ = > 1156 = x {}^{4} + \frac{1}{x {}^{4} } + 2(x {}^{2} )( \frac{1}{x {}^{2} } ) \\ = > 1156 = x {}^{4} + \frac{1}{x {}^{4} } + 2 \\ = > 1156 - 2 = x {}^{4} + \frac{1}{x {}^{4} } \\ = > 1154 = x {}^{4} + \frac{1}{x {}^{4} } \\ = > x {}^{4} + \frac{1}{x {}^{4} } = 1154\end{lgathered}
=>(x+
x
1
)
2
=x
2
+
x
2
1
+2(x)(
x
1
)
=>(3+2
3
+(3−2
3
))
2
=x
2
+
x
2
1
+2
=>(3+2
3
+3−2
3
)
2
=x
2
+
x
2
1
+2
=>(3+3)
2
=x
2
+
x
2
1
+2
=>(6)
2
=x
2
+
x
2
1
+2
=>36−2=x
2
+
x
2
1
=>34=x
2
+
x
2
1
s.o.b.s
=>(34)
2
=(x
2
+
x
2
1
)
2
=>1156=x
4
+
x
4
1
+2(x
2
)(
x
2
1
)
=>1156=x
4
+
x
4
1
+2
=>1156−2=x
4
+
x
4
1
=>1154=x
4
+
x
4
1
=>x
4
+
x
4
1
=1154