Question

if x + y = 8 and xy = 15/4 find the value of 5 (x² + y²) + 4 (x - y)​

Answer 1

Answer:

∴value of 5 (x² + y²) + 4 (x - y)​= 621/2

Step-by-step explanation:

here, it is given that

x + y= 8  ---------(i)

xy = 15/4 ----------(ii)

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

           = $8^{2}$ - 4* 15/4

           = 64 - 15$\sqrt{49}$

x - y=

x - y= 7 ---------(iii)

now, add equation ( i ) and ( iii ) , we get

= x + y + x - y= 8 + 7

= 2x= 15

= x = 15/2

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

= 15/2 + y = 8

= y = 8 - 15/2

= y = 1/2

∴ x= 15/2  and y= 1/2

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

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