Question

if a+1/a=17/4,find the value of (a-1/a)

Answer 1

I Hope This Helps U ^__^

Answer 2

Hi
Nice question

Question:-
a + 1/a = 17/4 , find the value of a - 1/a

Solution:-

a + 1/a = 17/4
(Squaring both sides)

(a + 1/a)² = (17/4)²

{Using identity
(x + y)² = x² + y² + 2xy}

a² + 1/a² + 2 × a × 1/a = 289/16
a² + 1/a² + 2 = 289/16
a² + 1/a² = 289/16 - 2
a² + 1/a² = 257/16

Now,
Squaring a - 1/a

(a - 1/a)² = a² + 1/a² - 2 × a × 1/a
(a - 1/a)² = 257/16 - 2
(a - 1/a)² = 225/16
a - 1/a = √225/16
a - 1/a = +15/4 or -15/4

Neglected -ve value

so

a - 1/a = 15/4

Hope this helps you.