Question

Factorise 3^50 + 3^49 - 9^24/3^48 + 3^27 - 9^23

Please help me
Urgently

The one who answer I'll follow him/her​

Answer 1

Correct Question :

Simplify-

[ 3⁵⁰ + 3⁴⁹ - 9²⁴]/[ 3⁴⁰ + 3²⁷ - 9²³ ]

Solution :

[ 3⁵⁰ + 3⁴⁹ - 9²⁴]/[ 3⁴⁰ + 3²⁷ - 9²³ ]

We can observe that some of the terms are in powers of 3 and some are in the powers of 9 .

We need to bring them to the same base to proceed .

This is known that 9 = 3²

So , a term of the form 9^k can be written as 3^(2k)

Using this ;

=> [ 3⁵⁰ + 3⁴⁹ - 3⁴⁸ ]/[ 3⁴⁰ + 3²⁷ - 3⁴⁶ ]

Now , we can see that the lowest power of 3 in the denominator is 3²⁷ .

Taking that common ; and cancelling we get

=> [ 3²³ + 3²² - 3²¹ ]/[ 3¹³ + 1 - 3²³ ]

Here , we have reached a dead end as nothing further can be cancelled .

We need two values , 3^23 and 3^13

3^23 = 9.41 × e10

=> 9.41 × e10 [ 1 + 1/3 - 1/9 ]

=> 9.41 × e10 { 1.22 }

=> ≈ 11.48 × e10

3^13 = 1594323

Denominator :

=> [ 1594323 + 1 + 9.41 × e10 ]

=> [ 9.4144 × e10 ]

{ The value of 3^13 is quite negligible than 3^23 , so the sum is close to 3^23 }

=> [ 11.48 / 9.41444 } as e10 gets cancelled

=> ≈ 1.22 approx .

This is the required answer .

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Note : Seems like the question is wrong : thinking :

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