Match the following with the value of a-2-1-a-2 for the conditions given below-14342711

The correct option is Using the identity, (a+b)^2 =a^2 + 2ab +b^2, a^2+b^2 =(a+b)^2 2ab. So, a^2+1/a^2 nbsp; = (a+1/a)^2 2 nbsp; nbsp; (i) Given that ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard IX

Mathematics

Expansion of (a ± b)²

Match the fol...

Question

Match the following with the value of $a^{2} + \frac{1}{a^{2}}$ for the conditions given below.

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

Using the identity,
$(a + b)^{2} = a^{2} + 2 a b + b^{2}$ ,
$a^{2} + b^{2} = (a + b)^{2} - 2 a b$ .

So, $a^{2} + \frac{1}{a^{2}} = (a + \frac{1}{a})^{2} - 2$

(i) Given that $a + \frac{1}{a} = 4$
$⟹ a^{2} + \frac{1}{a^{2}} = (a + \frac{1}{a})^{2} - 2 = 4^{2} - 2$
$a^{2} + \frac{1}{a^{2}} = 16 - 2 = 14$

(ii) Given that $a + \frac{1}{a} = 6$
$⟹ a^{2} + \frac{1}{a^{2}} = (a + \frac{1}{a})^{2} - 2 = 6^{2} - 2$
$a^{2} + \frac{1}{a^{2}} = 36 - 2 = 34$

Using identity,
$(a - b)^{2} = a^{2} - 2 a b + b^{2}$ ,
$a^{2} + b^{2} = (a - b)^{2} + 2 a b$ .
So, $a^{2} + \frac{1}{a^{2}} = (a - \frac{1}{a})^{2} + 2$

(iii) Given that $a - \frac{1}{a} = 5$
$⟹ a^{2} + \frac{1}{a^{2}} = (a - \frac{1}{a})^{2} + 2 = 5^{2} + 2 = 27$

(iv) Given that $a - \frac{1}{a} = 3$
$⟹ a^{2} + \frac{1}{a^{2}} = (a - \frac{1}{a})^{2} + 2 = 3^{2} + 2 = 11$

Suggest Corrections

Similar questions

Q. Match the following with the value of $a^2+\frac{1}{a^2}$ for the conditions given below.

Q. Match the following with the value of

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

for the conditions given below.

Q. Match the following for ellipse,

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, a > b

, with eccentricity

e .

Match the following for ellipse, $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, a > b$ with eccentricity $e$ .

Q. Let

A_{1}, A_{2}, . . ., A_{m}

be non-empty subsets of

{1, 2, 3, . . ., 100}

satisfying the following conditions:
(1) the numbers

| A_{1} |, | A_{2} |, . . ., | A_{m} |

are distinct ;
(2)

A_{1}, A_{2}, . . ., A_{m}

are pairwise disjoint.
(Here

| A |

denotes the number of elements in the set

A

).
Then the maximum possible value of

m

Join BYJU'S Learning Program

Match the following with the value of a2+1a2 for the conditions given below.

Match the following with the value of $a^{2} + \frac{1}{a^{2}}$ for the conditions given below.