If a -1- a -2 -3- then find the value of a 3-1- a 3A- 0B- -3- 18 -3D- 9 -3

The correct option is C 18√(3) a^3+1/a^3=(a+1/a)^3 3× a×1/a×(a+1/a) =(a+1/a)^3 3(a+1/a) Now, put the value of a+1/a in the above expression, we get (2√(3))^3 3 ...

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Byju's Answer

Standard VIII

Mathematics

Finding Square Root through Repeated Subtraction

If a +1/ a =2...

Question

If $a + \frac{1}{a} = 2 \sqrt{3}$ , then find the value of $a^{3} + \frac{1}{a^{3}}$

$0$

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$18 \sqrt{3}$

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$9 \sqrt{3}$

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$\sqrt{3}$

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Solution

The correct option is B
$18 \sqrt{3}$

$a^{3} + \frac{1}{a^{3}} = {(a + \frac{1}{a})}^{3} - 3 \times a \times \frac{1}{a} \times (a + \frac{1}{a})$

$= {(a + \frac{1}{a})}^{3} - 3 (a + \frac{1}{a})$

Now, put the value of $a + \frac{1}{a}$ in the above expression, we get

$(2 \sqrt{3})^{3} - 3 \times 2 \sqrt{3} = 24 \sqrt{3} - 6 \sqrt{3} = 18 \sqrt{3}$

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If a+1a=2√3, then find the value of a3+1a3

The correct option is B 18√3 a3+1a3=(a+1a)3−3×a×1a×(a+1a) =(a+1a)3−3(a+1a) Now, put the value of a+1a in the above expression, we get (2√3)3−3×2√3=24√3−6√3=18√3

If $a + \frac{1}{a} = 2 \sqrt{3}$ , then find the value of $a^{3} + \frac{1}{a^{3}}$