Question

The number x is 2 more than the number y. If
the sum of the squares of x and y is 34; find
the product of x and y.​

Answer 1

Answer:

x y = 15

Step-by-step explanation:

  x = y + 2

      x² + y² = 34

    x - y = 2

  squaring,  (x - y)² = 2²

            x² + y² - 2 x y = 4

            34 - 2 x y = 4

              x y = 15

Answer 2

Answer:15

Step-by-step explanation:

According to the question x=2+y

x²+y²=34

Now substitute 2+y for x in the above eq.

(2+y)²+y²=34

Expanding it we get,

4+y²+4y+y²=34

2y²+4y+4=34

y²+2y+2=17

y²+2y-15=0

By splitting the middle term we get,

y²-3y+5y-15=0

y(y-3)+5(y-3)=0

(y-3)(y+5)=0

Rejecting the negative value we get,

y=3

x=2+y=2+3=5

Product=xy=15

Hope it helps :)