If a-1-a-3- then the value of a2-1-a2 isA- 7B- 9C- 3D- 27

The correct option is A 7Using the identity, (a+b)^2 = a^2 + 2ab + b^2, (a + 1/a)^2 = a^2+ 2 × a×1/a+1/a^2 ⇒ 3^2= (a^2 +1/a^2) + 2 ⇒ nbsp; (a^2+1/a^2) = 7. ...

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Byju's Answer

Standard VIII

Mathematics

Applying Difference of Squares as a Product of Its Sum and Difference

If a+1/a=3, t...

Question

If $a + \frac{1}{a} = 3$ , then the value of $a^{2} + \frac{1}{a^{2}}$ is:_____.

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Solution

The correct option is A 7
Using the identity, $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ ,

$(a + \frac{1}{a})^{2} = a^{2} + 2 \times a \times \frac{1}{a} + \frac{1}{a^{2}}$
$\Rightarrow$ $3^{2} = (a^{2} + \frac{1}{a^{2}}) + 2$
$\Rightarrow$ $(a^{2} + \frac{1}{a^{2}}) = 7$ .

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If a+1a=3, then the value of a2+1a2 is:_____.

The correct option is A 7Using the identity, (a+b)2=a2+2ab+b2, (a+1a)2=a2+2× a×1a+1a2 ⇒ 32=(a2+1a2)+2 ⇒ (a2+1a2)=7.

If $a + \frac{1}{a} = 3$ , then the value of $a^{2} + \frac{1}{a^{2}}$ is:_____.

The correct option is A 7
Using the identity, $(a + b)^{2} = a^{2} + 2 a b + b^{2}$ ,

$(a + \frac{1}{a})^{2} = a^{2} + 2 \times a \times \frac{1}{a} + \frac{1}{a^{2}}$
$\Rightarrow$ $3^{2} = (a^{2} + \frac{1}{a^{2}}) + 2$
$\Rightarrow$ $(a^{2} + \frac{1}{a^{2}}) = 7$ .