Question

lf a2-6a-1=0 find a2+1/a2

Answer 1

Given: The expression a^2 - 6a - 1 = 0

To find: The value of a^2 + 1/a^2

Solution:

• Now we have given the expression as:

                 a^2 - 6a - 1 = 0

• We can write it as:

                 a^2 - 1 = 6a .................(i)

• Now we have: a^2 + 1/a^2

• We can write it as:

                 ( a - 1/a )^2 + 2

                 (a^2 - 1 / a)^2 + 2

• Putting (i) in above, we get:

                 (6a/a)^2 + 2

                 36 + 2

                 38

Answer:

             So the value of the given expression is 38.

Answer 2

GIVEN :

The equation is $a^2-6a-1=0$

TO FIND :

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

SOLUTION :

Given equation is $a^2-6a-1=0$

Now to find the value of the given expression as below :

Solving $a^2-6a-1=0$

Dividing the above equation by 'a' on both the sides we get,

$\frac{a^2-6a-1}{a}=\frac{0}{a}$

$\frac{a^2}{a}-\frac{6a}{a}-\frac{1}{a}=0$

$a-6-\frac{1}{a}=0$

$a-\frac{1}{a}=6$

Squaring on both sides

$(a-\frac{1}{a})^2=6^2$

By using the Algebraic identity :

$(a-b)^2=a^2-2ab+b^2$

Here a=a and $b=\frac{1}{a}$ and substituting the values in the above formula  we get,

$a^2-2(a)(\frac{1}{a})+(\frac{1}{a})^2=36$

$a^2-2+\frac{1}{a^2}=36$

$a^2+\frac{1}{a^2}=36+2$

$a^2+\frac{1}{a^2}=38$

∴ the value of $a^2+\frac{1}{a^2}$ is 38.