Math, asked by asmit50, 1 year ago

a^2-3a+1=0 find a^2+1/a^2​

Answers

Answered by tahseen619
13

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

Answered by anindyaadhikari13
22

\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
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