Question

If x2+ y2 = 37 and xy = 6: find:
6: find: 1) x + y 2) x - y 3) x2 - y2
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Answer 1

Answer:

(i)7 (ii)5  (iii) 35

Step-by-step explanation:

x²+y² =37  xy=6

(i)    (x+y)² = x²+y²+2xy

(x+y)² = 37+2*6 =49

x+y = 7

(ii)    (x-y)² = x²+y²-2xy

       (x-y)² = 37 -2*6

        (x-y)² = 25

       x-y =5

(iii)    x²-y² = (x+y)(x-y)

                  = 7*5 =35

Answer 2

Answer:

1) x + y = 7

2) x - y = 5

3) x²- y² = 35.  

Step-by-step explanation:

given x²+y²=37 and xy=6

1) we know (x+y)²=x²+y²+2xy

substituting given values in the above equation

(x+y)²=(x²+y²)+2xy

(x+y)²=37+2*6

(x+y)²=37+12

x+y = $\sqrt{49}$ =7

therefore the value of x+y = 7

2) we know (x-y)²=x²+y²-2xy

substituting given values in the above equation

(x-y)²=(x²+y²)-2xy

(x-y)²=37-2*6

(x-y)²=37-12

(x-y)²=25

x-y=$\sqrt{25}$ =5

therefore  the value of x-y = 5

3) we know x²- y² = (x+y)(x-y)

substituting x+y = 7 and x-y = 5 in above equation

x²- y² = (x+y)(x-y)

x²- y² = (7)(5)  

x²- y² = 35    

therefore  the value of  x²- y² = 35.