Answer:
Marco's age is 7 years old
Step-by-step explanation:
Let
x ----> Marco's age
y ----> Paolo's age
we know that
[tex]x=y-8[/tex] ----> [tex]y=x+8[/tex] ----> equation A
[tex]xy=105[/tex] ----> equation B
substitute equation A in equation B
[tex]x(x+8)=105[/tex]
[tex]x^2+8x-105=0[/tex]
Solve the quadratic equation
The formula to solve a quadratic equation of the form
[tex]ax^{2} +bx+c=0[/tex]
is equal to
[tex]x=\frac{-b(+/-)\sqrt{b^{2}-4ac}} {2a}[/tex]
in this problem we have
[tex]x^2+8x-105=0[/tex]
so
[tex]a=1\\b=8\\c=-105[/tex]
substitute in the formula
[tex]x=\frac{-8(+/-)\sqrt{8^{2}-4(1)(-105)}} {2(1)}[/tex]
[tex]x=\frac{-8(+/-)\sqrt{484}} {2}[/tex]
[tex]x=\frac{-8(+/-)22} {2}[/tex]
[tex]x=\frac{-8(+)22} {2}=7[/tex]
[tex]x=\frac{-8(-)22} {2}=-15[/tex]
Remember that the solution cannot be a negative number
so
The solution is x=7
therefore
Marco's age is 7 years old
