Question

3
2. Given: x - y = 5 and x2 + y2 = 73, find xy.​

Answer 1

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Answer 2

Answer:

x=(-3,8) y=(-8,3)

Step-by-step explanation:

We can do this by using substitution,

x-y=5.....(i)            x2+y2=73....(ii)

or, y=5-x.....(iii)

Substituting (iii) in (ii)

x2+(5-x)2=73

x2+25-10x+x2=73

2x2-10x+25-73=0

2x2-10x-48=0

2x2-16x+6x-48=0

2x(x-8)+6(x-8)=0

(2x+6)(x-8)=0

We got two values of x now...

2x+6 or x-8

x= -3 or x=8

Now we will be putting the values of x to find y.

x-y=5

-3-y=5   or 8-y=5

-y=5+3  or -y=5-8

y=-8      or -y=-3

            or y=3

So, we get the values of x and y.

x=(-3,8) y=(-8,3)

I hope the answer helps you.

Good luck!!