17. If 3a +1/3a = 2√3. evaluate
3a-1/3a
Answers
Answer:
3a+
3a
1
=2
3
−−−(1)
\begin{gathered} \Big( 3a - \frac{1}{3a}\Big)^{2} \\= \Big( 3a + \frac{1}{3a}\Big)^{2} - 4 \times (3a)\times \frac{1}{3a}\\= (2\sqrt{3})^{2} - 4 \\= 12 - 4 \\= 8 \end{gathered}
(3a−
3a
1
)
2
=(3a+
3a
1
)
2
−4×(3a)×
3a
1
=(2
3
)
2
−4
=12−4
=8
\begin{gathered} \implies \Big( 3a - \frac{1}{3a}\Big)= \sqrt{8} \\= 2\sqrt{2} \: --(2) \end{gathered}
⟹(3a−
3a
1
)=
8
=2
2
−−(2)
\begin{gathered} Now, 9a^{2} + \frac{1}{9a^{2}}\\= (3a)^{2} + \frac{1}{(3a)^{2}}\\= \Big(3a + \frac{1}{3a}\Big)^{2} - 2 \times (3a) \times \frac{1}{(3a)} \\= (2\sqrt{3})^{2} - 2 \\= 12 - 2 \\= 10 \end{gathered}
Now,9a
2
+
9a
2
1
=(3a)
2
+
(3a)
2
1
=(3a+
3a
1
)
2
−2×(3a)×
(3a)
1
=(2
3
)
2
−2
=12−2
=10
Step-by-step explanation:
Given,
3a+1/3a=2√3
(3a-1/3a)^2=(3a+1/3a)^2 - 2×3a×1/3a
(3a-1/3a)^2=(2√3)^2-2
(3a-1/3a)^2=12-2
(3a-1/3a)^2=10
3a-1/3a=√10
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