Question

If m+1/m=√3, calculate the simplified values of m²+1/m² and m³+1/m³​

Answer 1

Answer:

Use doubtnut app to solve the problem

Answer 2

Answer:

$m^2 + \frac{1}{m^2} = 1$ and $m^3 + \frac{1}{m^3} = 0$

Step-by-step explanation:

Given that:

$m + \frac{1}{m} = \sqrt{3}$

i) Now, $( m + \frac{1}{m})^{2} = m^2 + \frac{1}{m^2} + 2$

Substitute the given values:

=> $(\sqrt[]{3})^2 = m^2 + \frac{1}{m^2} + 2$

=>$3 = m^2 + \frac{1}{m^2} + 2$

=> $1 = m^2 + \frac{1}{m^2}$

Similarly,

ii) $( m + \frac{1}{m})^{3} = m^3 + \frac{1}{m^3} + 3(m + \frac{1}{m})$

Substitute the values:

=> $( \sqrt{3} })^{3} = m^3 + \frac{1}{m^3} + 3(\sqrt{3} )$

=>$3\sqrt{3} = m^3 + \frac{1}{m^3} + 3\sqrt{3}$

=> $0 = m^3 + \frac{1}{m^3}$