Question

if 3x-4y=5 and xy=5 find the value of (3x+4y)2​

Answer 1

Answer:

265

Step-by-step explanation:

Given---> 3x - 4y = 5 and xy = 5

To find---> Value of ( 3x + 4y )²

Solution---> We have an identity as follows,

1) ( a + b )² = a² + b² + 2ab

2) ( a - b )² = a² + b² - 2ab

Now, applying second identity , we get,

( 3x - 4y )² = ( 3x )² + ( 4y )² - 2 ( 3x ) ( 4y )

= 9x² + 16 y² - 24 xy

Putting 3x - 4y = 5 and xy = 5 , we get,

=> ( 5 )² = 9x² + 16y² - 24 ( 5 )

=> 25 = 9x² + 16y² - 120

=> 25 + 120 = 9x² + 16y²

=> 145 = 9x² + 16y²

=> 9x² + 16y² = 145

Now, applying first identity, we get,

( 3x + 4y )² = ( 3x )² + ( 4y )² + 2 ( 3x ) ( 4y )

= 9x² + 16y² + 24xy

= ( 9x² + 16y² ) + 24 ( xy )

Putting value of 9x² + 16y² and xy , we get,

= ( 145 ) + 24 ( 5 )

= 145 + 120

( 3x + 4y )² = 265

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