Question

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

Answer 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.

: )

Answer 2

Answer:

$\huge\bigstar\huge\tt\underline\red{ᴀɴsᴡᴇʀ }\bigstar$

Here is your answer

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

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

To find the value of:-

$5( {x}^{2} + {y}^{2} ) + 4(x - y)$

Hope it helps you..!!!

_________________

Thankyou:)