Question

a^2-3a+1=0 find a^2+1/a^2​

Answer 1

7

Step-by-step explanation:

Given:

a² - 3a + 1 = 0

To find:

a² + 1/a²

How to get Answer ?

1. First analyse the question,

2. Solve the given,

3. Do Multiplication, Division, Square, Cube As required.

4. Use Algebra Formula.

5. Simplify till answer.

Solution:

${a}^{2} - 3a + 1 = 0 \\ \\ {a}^{2} + 1 = - 3a$

[Dividing both side by a]

${a}^{} + \dfrac{1}{a} = - 3$

[Squaring both side]

$(a + \frac{1}{a} ) {}^{2} = { - 3}^{2} \\ \\ {a}^{2} + \frac{1}{ {a}^{2} } + 2.a. \frac{1}{a} = 9 \\ \\ {a}^{2} + \frac{1}{ {a}^{2} } + 2 = 9 \\ \\ {a}^{2} + \frac{1}{ {a}^{2} } = 9 - 2 \\ \\ \boxed{{a}^{2} + \frac{1}{ {a}^{2} } = 7}$

Therefore, the required answer is 7.

Algebra Formula Used

(a+b)² = a² + b² + 2ab

Answer 2

$\star\:\:\bf\large\underline\blue{Given,}$

• ${a}^{2} - 3a + 1 = 0$

$\star\:\:\bf\large\underline\blue{To find:-}$

• ${a}^{2} + \frac{1}{ {a}^{2} }$

$\star\:\:\bf\large\underline\blue{Solution:-}$

${a}^{2} - 3a + 1 = 0$

$\implies {a}^{2} + 1 = 3a$

Now, dividing both side by $a$, we get,

$\frac{ {a}^{2} + 1 }{a} = \frac{3 \cancel{a}}{ \cancel{a} }$

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

Now, squaring both side, we get,

${(a + \frac{1}{a} )}^{2} = {3}^{2}$

$\implies {a}^{2} + \frac{1}{ {a}^{2} } + 2 \times \cancel{a} \times \frac{1}{ \cancel{a}} = 9$

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

$\implies {a}^{2} + \frac{1}{ {a}^{2} } = 9 - 2$

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

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

$\star\:\:\bf\large\underline\blue{Answer:-}$

• ${a}^{2} + \frac{1}{ {a}^{2} } =7$