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

Answers ( )

    0
    2021-09-16T16:35:09+00:00

    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.

    : )

    0
    2021-09-16T16:35:39+00:00

    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:)

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