Question

if 3x+4y=16 and 3x-4y=4 find the value of xy. algebraic identities.

Answer 1

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We know the algebraic identity

a² + b² - 2ab = ( a - b )²

Or

a² + b² = ( a - b )² + 2ab

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It is given that ,

3x + 4y = 10 ----( 1 )

xy = -1 --------( 2 )

Now ,

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

9x² + 16y² = ( 3x - 4y )² + 24xy

= ( 10 )² + 24 × ( -1 )

= 100 - 24

= 76

I hope this helps you .

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Answer 2

3x+4y=16
3x-4y=4

after cancelling we get
8y=12
y=3/2

3x-4y=4
3x-4×3/2 =4
x=10/3

therefore x= 3.33
and y= 1.5