Question

The product of a number decreased by 1 and the same number increased by 2 is 70. Find all numbers that satisfy this condition.The solution set is(Use a comma to separate answers as needed.)

Answer 1

Write the relation given in statement as follows.

$(x-1)(x+2)=70$

On solving this,

$\begin{gathered} x^2-x+2x-2=70 \\ x^2+x-2-70=0 \\ x^2+x-72=0 \end{gathered}$

Write this equation as (x+9)(x-8)=0

Hence the solution set is

$\mleft\lbrace-9,8\mright\rbrace$