Question

if a^2 +9/a^2=31 , what is value of a -3/a​

Answer 1

Question :---- if a² + 9/a² = 31 , Find the value of (a - 3/a) ?

Formula used :---

→ a² + b² - 2ab = (a-b)²

Solution :---

it is given that (a)² + (9/a²) = 31

or,

→ (a)² + (3/a)² = 31

Subtracting (2*a*a/3) both sides we get ,

→ (a)² + (3/a)² - (2*a*a/3) = 31 - (2*a*a/3)

→ (a)² + (3/a)² - 2*(a)*(a/3) = 31 - 6

Now, we see that, LHS is in the form of a² + b² - 2ab,

So,

→ (a - 3/a)² = 25

Square root both sides now, we get,

→ (a - 3/a) = ±5

Hence, value of (a - 3/a) is ±5..

Answer 2

Answer:

Step-by-step explanation:

We Have :-

a² + 9 / a² = 31

To Find :-

a - 3 / a

Solution :-

( a )² + ( 3 / a )² = 31

Now subtracting ( 2a² / 3 ) from both sides

( a )² + ( 3 / a )² - 2 * ( a ) * ( a / 3 ) = 31 - 6

( a - 3 / a )² = 25

Square root both sides

a - 3 / a = ± 5