Question

if a2+1/a2=23 find the values of a+1/a​

Answer 1

Step-by-step explanation:

a2+ 1/a2 =23

a2 + (1/a2)2 = 23

since, by using identity a2 + b2 = (a+b)2 - 2ab

now,

(a+1/a2)2 - 2× a× 1/a = 23

(a)2 + (1/a)2 + 2×a × 1/a -2×a×1/a = 23

(a)2 + (1/a)2 +2a/a -2a/a =23

since (+2a/a -2a/a) = 23

so, (a)2 + (1/a)2 =23

now,.....

(a+1/a)2 = 23

a+1/a =√23

hence, the value of a+1/a =√23

Answer 2

given

${a}^{2} + \frac{1}{ {a}^{2} } = 23$

adding 2 both sides

${a}^{2} + \frac{1}{ {a}^{2} } + 2 = 25 \\ \\ ( {a + \frac{1}{a} })^{2} = 25 \\ \\ a + \frac{1}{a} = ±5$