Question

if a^2- 3a =1 find the value of
(i). a-1/a
(ii) a+1/a
Dear if u knw the answer plz let me knw asap!!​

Answer 1

Step-by-step explanation:

Given :-

a²-3a = 1

To find :-

find the value of the following :

(i). a-1/a

(ii) a+1/a

Solution :-

Given Quadratic equation is a²-3a = 1

It can be written as

=> a²-(2/2)(3a) = 1

=> a²-2(a)(3/2) = 1

On adding (3/2)² both sides then

=> a²-2(a)(3/2)+(3/2)² = 1+(3/2)²

=> [a-(3/2)]² = 1+(9/4)

Since (a-b)² = a²-2ab+b²

=> [a-(3/2)]² = (4+9)/4

=> [a-(3/2)]² = 13/4

=> a-(3/2) = ±√(13/4)

=> a -(3/2) = ±√13 /2

=> a = (±√13/2)+(3/2)

=> a = (±√13+3)/2

=> a = (√13+3)/2 or (-√13+3)/2

Now, Take a = (√13+3)/2 then

=> 1/a = 1/[ (√13+3)/2 ]

=> 1/a = 2/(√13+3)

The Rationalising factor of√13+3 is √13-3

=> 1/a = [2/(√13+3)]×[(√13-3)/(√13-3)]

=> 1/a = [2×(√13-3)]/[(√13+3)(√13-3)]

=> 1/a = [ 2×(√13-3)]/[(√13)²-(3)²]

Since, (a+b)(a-b) = a²-b²

=> 1/a = [2×(√13-3)]/(13-9)

=> 1/a = [2×(√13-3)]/4

=> 1/a = (√13-3)/2 -----------(1)

Now,

i)a-(1/a)

=> [(√13+3)/2 ]- [(√13-3)/2]

=> [(√13+3)-(√13-3)]/2

=> (√13+3-√13+3)/2

=> (3+3)/2

=> 6/2

=> 4

a-(1/a) = 4

and

ii) a+(1/a)

=> [(√13+3)/2 ]+ [(√13-3)/2]

=> [(√13+3)+(√13-3)]/2

=> (√13+3+√13-3)/2

=> (√13+√13)/2

=>2√13/2

=> √13

a+(1/a) = √13

Answer:-

i) The value of a-(1/a) is 4

ii) The value of a+(1/a) is √13

Used formulae:-

→(a-b)² = a²-2ab+b²

→(a+b)(a-b) = a²-b²

→The Rationalising factor of√a+b is √a-b

→The Rationalising factor of√a-b is √a+b

Note :-

If we take a = (-√13+3)/2 then we get same values for a-(1/a) and a+(1/a).

Used Method:-

→Completing the square method

Answer 2

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Step-by-step explanation:

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