Palidrom

A number consists of two digits whose product is 24. When 18 is subtracted from the number, the digits change their places. Find the number.

Correct answer:

x =  64

Step-by-step explanation:

$$\begin{gathered} a=10a+b \\ a\cdot b=24 \\ 10a+b-18=10b+a \\ 9a-18=9b \\ a-2=b \\ a-b=2 \\ a\cdot (a-2)=24 \\ a\cdot (a-2)=24 \\ {a}^2-2a-24=0 \\ p=1;q=-2;r=-24 \\ D=q^2-4pr=2^2-4\cdot 1\cdot (-24)=100 \\ D>0 \\ {a}_{1,2}=\frac{-q\pm \sqrt{D}}{2p}=\frac{2\pm \sqrt{100}}{2} \\ {a}_{1,2}=\frac{2\pm 10}{2} \\ {a}_{1,2}=1\pm 5 \\ {a}_1=6 \\ {a}_2=-4 \\ a=a_1=6 \\ b=a-2=6-2=4 \\ x=10\cdot a+b=10\cdot 6+4=64 \end{gathered}$$

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