Question

If (x+y) 2 = 100 and (x-y) 2 =36 then find the value of ‘x’ and ‘y’ , (x>y)​

Answer 1

Given :- If (x+y)² = 100 and (x-y)² = 36 then find the value of ‘x’ and ‘y’ , (x>y) .

Solution :-

we know that,

• (x + y)² - (x - y)² = 4xy

so, putting given values we get,

→ 4xy = (x + y)² - (x - y)²

→ 4xy = 100 - 36

→ 4xy = 64

→ xy = 16 .

now, given that, x > y

• x = 16, y = 1
• x = 8, y = 2

at x = 16 and y = 1,

→ (x + y)² = (16 + 1)² = 17² = 289 ≠ 100

and, at x = 8 and y = 2,

→ (x + y)² = (8 + 2)² = 10² = 100

also,

→ (x - y)² = (8 - 2)² = 6² = 36 .

therefore, value of x is 8 and y is 2 .

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Answer 2

Given :  (x+y)²  = 100 and (x-y)² =36  

To find :    the value of ‘x’ and ‘y’ , (x>y)​

Solution:

(x-y)² =36  

=> x - y  = ±6

x > y   is given  => x - y is +ve

Hence  x - y  = 6

 (x+y)²  = 100

=> x + y  = ±10

Case 1 : x  + y  = 10     and case 2 :  x  + y  = - 10

x  + y  = 10

x - y  = 6

=> x = 8   and  y = 2

x  + y  = - 10

x - y  = 6

=> x = - 2   and  y = - 8

Hence ( x, y)  is  (  8 , 2)  or ( - 2 , - 8)

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