## if x+y =8 and xy= 3 3/4 find the value of 5(x^2+y^2)+4(x-y)​

Question

if x+y =8 and xy= 3 3/4 find the value of 5(x^2+y^2)+4(x-y)​

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1 month 2021-09-16T16:33:54+00:00 2 Answers 0 views 0

1. Step-by-step explanation:

Hi ,

It is given that ,

x + y = 8 —( 1 )

xy = 15/4 —( 2 )

( x – y )² = ( x + y )² – 4xy

= 8² – 4 × 15/4

= 64 – 15

( x – y )² = 49

x – y = 7 —( 3 )

add equation ( 1 ) and ( 3 ) , we get

2x = 8 + 7

2x = 15

x = 15/2

put x = 15/2 in equation ( 1 ) , we get

15/2 + y = 8

y = 8 – 15/2

y = ( 16 – 15 )/2

y = 1/2

Therefore ,

x = 15/2 , y = 1/2

Now ,

i ) x – y = 7 [ from ( 3 ) ]

ii ) 3( x² + y² )

= 3 [ ( x + y )² – 2xy ]

= 3 [ 8² – 2 × 15/4 ]

= 3 [ 64 – 15/2 ]

= 3 ( 128 – 15 )/2

= ( 3 × 113 )/2

= 339/2

iii ) 5[ ( x² + y² ) + 4 ( x – y ) ]

= 5 [ ( x + y )² – 2xy ] + 4 ( x – y ) ]

= 5 [ 8² – 2 × 15/4 ] + 4 × 7

= 5 [ 64 – 15/2 ] + 28

= 5 × 113/2 + 28

= 565/2 + 28

= ( 565 + 56 )/2

= 621/2

I hope this helps you.

: ) kindly see the image above attach for complete solution step by step:-

Given:-x+y=8;xy=15/4

To find the value of:- Hope it helps you..!!!

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Thankyou:)