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

x=y+2

x²+y²=34
(y+2)²+y²=34
y²+4+4y+y²=34
2y²+4y+4=34
y²+2y+2=17
y²+2y=15
y²+2y-15=0
y²+5y-3y-15=0
y(y+5)-3(y+5)=0
(y-3)(y+5)=0

∴ y=3
    y= -5

x=y+2

1st case:
x=3+2
x=5

2nd case
x= -5+2
x= -3

Answer 2

Answer:

15

Step-by-step explanation:

As given, x = y + 2   & x² + y² = 34

    Case 1 :

⇒ x = y + 2

⇒ x - y = 2

            Square on both sides:

⇒ (x - y)² = 2²

⇒ x² + y² - 2xy = 4

⇒ 34 - 2xy = 4

⇒ 34 - 4 = 2xy

⇒ 30/2 = xy

⇒ 15 = xy = product of x and y