Question

a square + 1 by a square is equal to 23 find the value of a + 1 by a​

Answer 1

Question: a² + 1/a² = 23
Find the value of a + 1/a ?

Solution:
As we know, (a + b)² = a² + b² + 2ab
So, a² + b² = (a + b)² - 2ab

Now, Suppose b = 1/a, then the formula changes to:
a² + 1/a² = (a + 1/a)² - 2a(1/a)
23 = (a + 1/a)² - 2a/a
23 = (a + 1/a)² - 2
(a + 1/a)² = 23 + 2 = 25
Thus, (a + 1/a) = ±5

Hence, (a + 1/a) = (+5), and (-5)
So we got 2 answers of (a + 1/a)

(if you still have any doubt, feel free to comment.)
:)

Thankyou!!!

Answer 2

Answer:

Heya Friend !!

Here's ur answer wid solution :-

{a}^{2} + { (\frac{1}{a}) }^{2} = 23a

2

+(

a

1

)

2

=23

( {a + \frac{1}{a}) }^{2} = {a}^{2} + {( \frac{1}{a}) }^{2} + 2a \times \frac{1}{a}(a+

a

1

)

2

=a

2

+(

a

1

)

2

+2a×

a

1

[ using identity ( a + b )² = a² + b² + 2ab ]

( {a + \frac{1}{a} )}^{2} = 23 + 2(a+

a

1

)

2

=23+2

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

a

1

)

2

=25

a + \frac{1}{a} = \sqrt{25}a+

a

1

=

25

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

a

1

=5