Question

If a^2 -5a+1=0, then a^2 + 1/a^2 =

1) 25
2) 23
3) 27
4) 22

Answer 1

Answer:

B. 23

Step-by-step explanation:

Answer 2

Given

a² - 5a + 1 = 0

To Find :-

The value of $a\:+\: \dfrac{1}{a}$

Calculations

=> a² - 5a + 1 = 0

Dividing both side by a , we get

=> $a\:-5\:+\: \dfrac{1}{a}\:=\:0$

=> $a \:+\: \dfrac{1}{a} \:=\:5$

Squaring both sides , we get :-

=> ${(a \:+\: \dfrac{1}{a} \:)}^2 \:=\:25$

=> $a^2 \:+\: 2 \:+\:\dfrac{1}{a^2}\:=\:25$

=> $a^2 \:+\:\dfrac{1}{a^2}\:=\:23$

Hence, the correct option is B) 23.