Question

if m^2-3m-1=0 find m^2+1/m^2​

Answer 1

The point of this question is we can find some equivalent equation by MDAS:

• Multiplication
• Division
• Addition
• Subtraction

$m=0$ doesn't satisfy the equation. So, we can find an equivalent equation for $m$, by dividing by $m$.

$m^2-3m-1=0$

$\implies \dfrac{m^2-3m-1}{m} =0$

$\implies m-3-\dfrac{1}{m} =0$

$\therefore m-\dfrac{1}{m} =3$

Let's square both sides to find the value. [1]

$\implies (m-\dfrac{1}{m} )^2=3^2$

$\implies m^2-2\times \dfrac{\cancel{m}}{\cancel{m}} +\dfrac{1}{m^2} =9$

$\implies m^2-2+\dfrac{1}{m^2} =9$

$\therefore m^2+\dfrac{1}{m^2} =11$

More information:

[1] If we square both sides and solve the equation, the equation is not always equivalent.

• $m-\dfrac{1}{m} =3$ is $m^2-3m-1=0$
• $m^2+\dfrac{1}{m^2} =11$ is $m^4-11m^2+1=0$

The second equation is $(m^2+3m+1)(m^2-3m+1)=0$, so it gives extra solutions that do not belong. This means we get the same value for $m+\dfrac{1}{m} =3$ also.

The same goes for the square root equations since it requires to square both sides.

Answer 2

Answer:

The point of this question is we can find some equivalent equation by MDAS:

Multiplication

Division

Addition

Subtraction

m=0m=0 doesn't satisfy the equation. So, we can find an equivalent equation for mm , by dividing by mm .

m^2-3m-1=0m

2

−3m−1=0

\implies \dfrac{m^2-3m-1}{m} =0⟹

m

m

2

−3m−1

=0

\implies m-3-\dfrac{1}{m} =0⟹m−3−

m

1

=0

\therefore m-\dfrac{1}{m} =3∴m−

m

1

=3

Let's square both sides to find the value. [1]

\implies (m-\dfrac{1}{m} )^2=3^2⟹(m−

m

1

)

2

=3

2

\implies m^2-2\times \dfrac{\cancel{m}}{\cancel{m}} +\dfrac{1}{m^2} =9⟹m

2

−2×

m

m

+

m

2

1

=9

\implies m^2-2+\dfrac{1}{m^2} =9⟹m

2

−2+

m

2

1

=9

\therefore m^2+\dfrac{1}{m^2} =11∴m

2

+

m

2

1

=11

More information:

[1] If we square both sides and solve the equation, the equation is not always equivalent.

m-\dfrac{1}{m} =3m−

m

1

=3 is m^2-3m-1=0m

2

−3m−1=0

m^2+\dfrac{1}{m^2} =11m

2

+

m

2

1

=11 is m^4-11m^2+1=0m

4

−11m

2

+1=0

The second equation is (m^2+3m+1)(m^2-3m+1)=0(m

2

+3m+1)(m

2

−3m+1)=0 , so it gives extra solutions that do not belong. This means we get the same value for m+\dfrac{1}{m} =3m+

m

1

=3 also

The same goes for the square root equations since it requires to square both sides

.