If a -1- a -3- then the value of a 2-1- a 2 is-A- 7B- 11C- 4D- 9

The correct option is B 11Using 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 ⇒ (a^2 + 1/a^2) = 11. ...

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Byju's Answer

Standard VIII

Mathematics

Expansion of (a - b)^2

If a -1/ a =3...

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 C 11
Using the identity, $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ ,
$(a - \frac{1}{a})^{2} = a^{2} - 2 \times a \times \frac{1}{a} + \frac{1}{a^{2}}$
$\Rightarrow$ $3^{2} = (a^{2} + \frac{1}{a^{2}}) - 2$
$\Rightarrow$ $(a^{2} + \frac{1}{a^{2}}) = 11$ .

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Similar questions

Q. If

a + \frac{1}{a} = 3

, then the value of

a^{2} + \frac{1}{a^{2}}

is:_____.

Q. If

a^{2} + \frac{1}{a^{2}} = 11

, then find the value of

(a - \frac{1}{a})

Q. If

a = 9

, find the value of

a^{2} + \frac{1}{a^{2}}

Q. If

a^{2} - 4 a - 1 = 0, a \neq 0

, then the value of

a^{2} + 3 a + \frac{1}{a^{2}} - \frac{3}{a}

Q. Simplify

\frac{a^{2} + 3 a}{a^{2} + 4 a + 3} \times \frac{a^{2} - 2 a - 3}{a^{2} - 9}

, then the answer is

\frac{a}{a + 3}

If true then enter

1

and if false then enter

0

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

The correct option is C 11Using the identity, (a−b)2=a2−2ab+b2, (a−1a)2=a2−2×a×1a+1a2 ⇒ 32=(a2+1a2)−2 ⇒ (a2+1a2)=11.

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

The correct option is C 11
Using the identity, $(a - b)^{2} = a^{2} - 2 a b + b^{2}$ ,
$(a - \frac{1}{a})^{2} = a^{2} - 2 \times a \times \frac{1}{a} + \frac{1}{a^{2}}$
$\Rightarrow$ $3^{2} = (a^{2} + \frac{1}{a^{2}}) - 2$
$\Rightarrow$ $(a^{2} + \frac{1}{a^{2}}) = 11$ .