If a -1- a -3- then find the value of a 2-1- a 2 a 3-1- a 3A- 112B- 123C- 125D- 126

The correct option is D 126 Given, a+1/a=3 ... (i) Squaring both the sides, we get (a+1/a)^2=9 ⇒ a^2+1/a^2+2a.1/a=9 ⇒ a^2+1/a^2=9 2=7 ... (ii) Now, taking cube ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identity (a+b)^3

If a +1/ a =3...

Question

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

123

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126

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112

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Solution

The correct option is C
126

Given, $a + \frac{1}{a} = 3$ ... (i)

Squaring both the sides, we get

${(a + \frac{1}{a})}^{2} = 9$

$\Rightarrow a^{2} + \frac{1}{a^{2}} + 2 a . \frac{1}{a} = 9$

$\Rightarrow a^{2} + \frac{1}{a^{2}} = 9 - 2 = 7$ ... (ii)

Now, taking cube of equation (i), we get

${(a + \frac{1}{a})}^{3} = 27$

$\Rightarrow a^{3} + \frac{1}{a^{3}} + 3 a . \frac{1}{a} (a + \frac{1}{a}) = 27$

$\Rightarrow a^{3} + \frac{1}{a^{3}} + 3 \times 3 = 27$

$\Rightarrow a^{3} + \frac{1}{a^{3}} = 27 - 9 = 18$ ... (iii)

We have to find the value of $(a^{2} + \frac{1}{a^{2}}) (a^{3} + \frac{1}{a^{3}})$

$= 7 \times 18 = 126$

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