Question

if a+1/a = p and a is not equal to 0 then show that a cube +1/a cube = p ( p square -3)​

Answer 1

Step-by-step explanation:

Let the characteristic root of A be λ.

⇒∣A−λI∣=0

For P

−1

AP;

∣

∣

∣

P

−1

AP−λI

∣

∣

∣

=

∣

∣

∣

P

−1

AP−λP

−1

PI

∣

∣

∣

=

∣

∣

∣

P

−1

∣

∣

∣

∣A−λI∣∣P∣=∣A−λ1∣.

⇒λ is also characteristic roots of matrix P

−1

AP