Question

if X^2- Y^2= 28 and X-Y= 8 then average of X and Y is?​

Answer 1

Answer:

7/4

Step-by-step explanation:

(x+y) (x-y)= 28

x+y= 28/8 = 7/2

(x+y)/2= 7/4

Answer 2

⠀⠀ || ✪ ϙᴜᴇsᴛɪᴏɴ ✪ ||

if X²- Y² = 28 and X - Y= 8 then average of X and Y is ?

⠀⠀|| ☆.ANSWER.☆ ||

Given:-

• x² - y² = 28 ...........(1)
• x - y = 8 ................(2)

Find:-

• Average of x and y .

|| ☆.Explanation.☆ ||

We know,

★ ( x² - y² ) = (x - y)(x + y)

Keep value by equ(2), and equ(1)

➥ 28 = ( x + y)(8)

➥ ( x + y) = 28/8

➥ ( x + y ) = 7/2 ..............(3)

So, Average will be

➥ ( x + y )/2 = 7/4. [Ans]

Now, Calculate value of x and y.

Add equation(2) and equation (3)

➥ 2x = 7/2 + 8

➥ 2x = (7+16)/2

➥ 2x = 23/2

➥ x = 23/4

Keep value in equ(2),

➥ 23/4 - y = 8

➥ y = 23/4 - 8

➥ y = (23 - 32)/4

➥ y = -9/4

Thus:-

• Value of x = 23/4
• Value of y = -9/4

⠀|| ☆.Verification.☆ ||

keep value of x and y in equ(2),

➥ 23/4 - (-9)/4 = 8

➥ (23+9)/4 = 8

➥ 32/4 = 8

➥ 8 = 8

L.H.S. = R.H.S

And,

Verification for average of x and y

➥ ( x + y )/2

keep value of x and y

➥ [23/4 + (-9/4)]/2

➥ [(23-9)/4]/2

➥ 14/(4×2)

➥ 7/4

That's proved .