Question

if a²-5a+1=0 find a²+1/a²

tell me the correct answer step by step in copy I will mark you as brainliest ​

Answer 1

Answer: 23 is the answer.

Step-by-step explanation:

$a^2 - 5a + 1 = 0\\or, a^2 + 1 = 5a \\or, a + 1/a = 5\\or, a^2 + 2.a.1/a+1/a^2 = 25\\or, a^2 + 2 + 1/a^2 = 25\\or, a^2 + 1/a^2 = 25-2\\so, a ^2 + 1/a^2 = 23$

Answer 2

Given :

An equation $a^{2} -5a+1=0$

To find :

The value of the expression $a^{2} +\frac{1}{a^{2} }$

Step-by-step explanation:

• The value of the given expression value can be found by following these steps.
• By completion of square the value of a can be found.
• The formula used is,

       $-b$ ± $\frac{\sqrt{b^{2} -4ac}}{2a}$

• From the equation we know that,

      $a=1$ , $b=-5$ , $c=1$

• By substituting the values in the given equation,

      $-(-5)$ ± $\frac{\sqrt{(-5)^{2} -4(1)(1)} }{2(1)}$

• By removing the brackets,

       $5$ ± $\frac{\sqrt{25-4}}{2}$

• By subtracting the values and taking root,

      $5$ ± $\frac{4.5}{2}$

• By diving the values,

      $5$ ± $2.25$

• The 2 values can be split up by

      $5+2.25$ , $5-2.25$

• The values of a are

       $7.25$ , $2.75$

• The value of the expression must be found.
• Firstly, substitute $7.25$ in the given expression and then substitute $2.75$ in the given expression.

• Substituting $7.25$ in the expression

       $(7.25)^{2} +\frac{1}{(7.25)^{2}}$

• The square value of $7.25$ will be

       $52.56 + \frac{1}{52.56}$

• After dividing the values,

      $52.56+0.01$

• The final value of the expression will be $52.57$ when a is $7.25$
• Now, let's substitute the other value of a that is $2.75$

       $(2.75)^{2} +\frac{1}{(2.75)^{2}}$

• The square value of $2.75$ will be

       $7.56+\frac{1}{7.56}$

• After dividing the values,

      $7.56+0.13$

• The final value of the expression will be $7.69$ when a is $2.75$

Final answer :

The value of the expression $a^{2} +\frac{1}{a^{2} }$ is $7.69$ , $52.57$ when a is $7.25$ and $2.75$ respectively,