Question

Z +1/z=5 find the value of z^2+1/z^2​

Answer 1

Solution :-

We are provided with :-

$\star \sf{ z + \dfrac{1}{z} = 5 }$

The question ask the value of

$\star \sf{ z^2 + \left(\dfrac{1}{z}\right)^2 }$

We know

• a² + b² = (a + b)² - 2ab

By using the same

$\implies \sf{ z^2 + \left(\dfrac{1}{z}\right)^2 = \left( z + \dfrac{1}{z} \right)^2 - 2 }$

$\implies \sf{ z^2 + \left(\dfrac{1}{z}\right)^2 = (5)^2 - 2 }$

$\implies \sf{ z^2 + \left(\dfrac{1}{z}\right)^2 = 25 - 2 }$

$\implies \sf{ z^2 + \left(\dfrac{1}{z}\right)^2 = 23 }$