Question

If a+1/a=3 find a^2+1/a^2​

Answer 1

Question:

If a + 1/a = 3 then find the value of

x^2 + 1/x^2.

Answer:

a^2 + 1/a^2 = 7

Solution:

Note:

(x+y)^2 = x^2 + y^2 + 2•x•y

It is given that,

a + 1/a = 3 --------(1)

Now,

Squaring both sides of eq-(1), we get;

=> (a+1/a)^2 = a^2 + (1/a)^2 + 2•a•(1/a)

=> (3)^2 = a^2 + 1/a^2 + 2

=> 9 = a^2 + 1/a^2 + 2

=> a^2 + 1/a^2 = 9 - 2

=> a^2 + 1/a^2 = 7

Hence,

The required value of the a^2 +1/a^2 is

7.

Answer 2

Question →

$\mathfrak{if \: a + \frac{1}{a} = 3 \: then \: find \: {a}^{2} + \frac{1}{ {a}^{2} } }$

Answer→

$\implies \: \boxed{\mathfrak{ {a}^{2} + \frac{1}{ {a}^{2} } = 7}} \:$

Used Identity→

$\red{ \mathfrak{ \star \: {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy}}$

Solution :-

According to the question,

We have,

$\rightarrow \: \mathfrak{a + \frac{1}{a} = 3} \\ \\ \bf{squaring \: on \: both \: sides} \\ \\ \rightarrow \: \mathfrak{ { \bigg(a + \frac{1}{a} \bigg) }^{2} = {(3)}^{2} } \\ \\ \bf{ apply \: the \: given \: identity} \\ \\ \ \rightarrow \: \mathfrak{ {a}^{2} + \frac{1}{ {a}^{2} } + 2 \times a \times \frac{1}{a} = 9} \\ \\ \rightarrow \: \mathfrak{ {a}^{2} + \frac{1}{ {a}^{2} } + 2 = 9} \\ \\ \mathfrak{ \rightarrow \: {a}^{2} + \frac{1}{ {a}^{2} } = 9 - 2} \\ \\ \rightarrow \: \boxed{\mathfrak{ {a}^{2} + \frac{1}{ {a}^{2} } = 7}}$

Hope it helps you.