Question

If a²+1/a²=23,find the value of (a+1/a)​

Answer 1

Answer:

5

Step-by-step explanation:

By the formula,

(a+b)² = a²+b²+2ab

(a+1/a)² = a²+1/a² + 2×a×1/a

(a+1/a)² = 23+2

(a+1/a)² = 25

square rooting both sides,

√(a+1/a)² = √25

a+1/a = 5

Answer 2

Answer:

5

Step-by-step explanation:

${a}^{2} + \frac{1}{ {a}^{2} } = 23 \\ {a}^{2} + \frac{1}{ {a}^{2} } + 2 = 23 + 2 = 25$

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

So,

$a + \frac{1}{a} = 5$

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