Question

What adds up to 10 and multiplies into 12

Answer 1

8.606 and 1.394 add up to 10 and multiply to 12.

Answer 2

`x;\ y-the\ numbers\\\\ \left\{\begin{array}{ccc}x+y=10&\to x=10-y\\x\cdot y=12\end{array}\right\\\\\\subtitute\ x=10-y\ to\ the\ equation\ x\cdot y=12\\\\(10-y)\cdot y=12\\\\10y-y^2=12\ \ \ |subtract\ 12\ from\ bot\ sides\\\\-y^2+10y-12=0\ \ \ |change\ the\ signs\\\\y^2-10y+12=0`
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`Use\ the\ quadratic\ formula:ax^2+bx+c=0\\\Delta=b^2-4ac\\if\ \Delta \ \textgreater \ 0\ therefore\ solutions\ is:\ y_1=(-b-\sqrt\Delta)/(2a)\ and\ y_2=(-b+\sqrt\Delta)/(2a)`


`y^2-10y+12=0\\a=1;\ b=-10;\ c=12\\\\\Delta=(-10)^2-4(1)(12)=100-48=52\\√(\Delta)=√(52)=√(4\cdot13)=√(4)\cdot√(13)=2√(13)`


`y_1=(-(-10)-2√(13))/(2\cdot 1)=(10-2√(13))/(2)=\huge\boxed{5-√(13)}\\\\y_2=(-(-10)+2√(13))/(2\cdot1)=(10+2√(13))/(2)=\huge\boxed{5+√(13)}`


`subtitute\ the\ values\ of\`


`Your\ answer:\\\boxed{x=5+√(13)\ and\ y=5-√(13)\ or\ x=5-√(13)\ and\ y=5+√(13)}`