Question

The sum of two numbers is 10 and their product is 24. Find thenumbers.​

Answer 1

Answer:

6 and 4

Step-by-step explanation:

$x,\ y-\text{the numbers}\\\\(1)\qquad x+y=10\\\\(2)\qquad xy=24\\\\==================\\\\(1)\qquad x+y=10\qquad\text{subtract}\ y\ \text{from both sides}\\(*)\qquad x=10-y\\\\\text{Substitute to (2):}\\\\(10-y)y=24\qquad\text{ue the distributive property:}\ a(b+c)=ab+ac\\10y-y^2=24\qquad\text{subtract 24 from both sides}\\-y^2+10y-24=0\qquad\text{change the signs}\\y^2-10y+24=0\\y^2-6y-4y+24=0\\y(y-6)-4(y-6)=0\\(y-6)(y-4)=0\iff y-6=0\ or\ y-4=0\\\\y-6=0\qquad\text{add 6 to both sides}\\y=6\\\\y-4=0\qquad\text{add 4 to both sides}\\y=4$

$\text{Put the values of}\ y\ \text{to (*)}:\\\\\text{for}\ y=6:\\x=10-6=4\\\\\text{for}\ y=4:\\x=10-4=6$