Number difference

The difference between the two numbers is 82. The first number is eight, less than the square of the second number. Specify these numbers.

Final Answer:

a₁ =  73
b₁ =  -9
a₂ =  92
b₂ =  10

Step-by-step explanation:

$$\begin{gathered} a-b=82 \\ a=b^2-8 \\ {b}^2-8-b=82 \\ {b}^2-b-90=0 \\ {b}_1=-9 \\ {b}_2=10 \\ {a}_1=b_1^2-8=(-9{)}^2-8=73 \\ {a}_1=a_2=b_2^2-8=10^2-8=92=73 \end{gathered}$$

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