If a number x is 2 more than y and the sum of squares of x and y is 34.
Find the product of x and y.
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Given that,
x=2+y—————— 1
x^2+y^2=34
(2+y)^2+y^2=34
2^2+y^2+y^2+4y=34
4+2y^2+4y=34
2y^2+4y-30=0
Dividing the whole equation by 2
y^2+2y-15=0
y^2+5y-3y-15=0
y(y+5)-3(y+5)=0
(y+5)(y-3)=0
y+5=0,y-3=0
y=-5,y=3
Substituting y=-5 and y=3 on eq 1
x=2+(-5)=2-5 , x=2+3
x=-3,x=5
x*y=(-5)*(-3)=15, x*y=3*5=15
So the product of x and y is 15
x=2+y—————— 1
x^2+y^2=34
(2+y)^2+y^2=34
2^2+y^2+y^2+4y=34
4+2y^2+4y=34
2y^2+4y-30=0
Dividing the whole equation by 2
y^2+2y-15=0
y^2+5y-3y-15=0
y(y+5)-3(y+5)=0
(y+5)(y-3)=0
y+5=0,y-3=0
y=-5,y=3
Substituting y=-5 and y=3 on eq 1
x=2+(-5)=2-5 , x=2+3
x=-3,x=5
x*y=(-5)*(-3)=15, x*y=3*5=15
So the product of x and y is 15
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