Question

If a+1/a=17/4. Find the value of (a-1/a)
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Answer 1

Answer:

(-15/4),(15/4)

Step-by-step explanation:

Given:-

$a + \frac{1}{a} = \frac{17}{4}$

To Find:-

$a - \frac{1}{a}$

Solution:-

a+1/a=17/4

Taking LCM:-

(a²+1)/a=17/4

Cross Multiplying Both Side:-

4(a²+1)=17(a)

4a²+4=17a

4a²-17a+4=0

4a²-16a-a+4=0

4a(a-4)-1(a-4)=0

(4a-1)(a-4)=0

a=(1/4),4

When a=(1/4),

a-(1/a)=(1/4)-(1 / 1/4)=(1/4)-4=(1-16)/4=(-15/4)

When a=4

a-(1/a)=4-(1/4)=(16-1)/4=15/4

Answer 2

Step-by-step explanation:

a + 1/ a = 17/4

we know that

(a-1/a)^2 = (a+1/a)^2 -4

= 17/4)^2 - 4

= 289/16 - 4

= 225 / 16

= (15/4) ^2