Answer:
The numbers for which the given property hold true are 12 and -7
Step-by-step explanation:
Let the number be [tex]x[/tex].
As per the given statement:
Square of the number ([tex]x^{2}[/tex]) is 84 more than five times of the number ([tex]5x+84[/tex]).
Writing in the equation form:
[tex]x^{2} =5x+84[/tex]
To find:
All the numbers for which above equation holds true.
Solution:
[tex]x^{2} =5x+84[/tex]
Let us solve the above equation by rearranging the terms and then let us find the roots of the equation.
It is a quadratic equation(i.e. maximum power of [tex]x[/tex] is 2) so it will have 2 solutions i.e. 2 values of [tex]x[/tex] for which the above equation will hold true.
[tex]x^{2} -5x-84=0[/tex]
Let us factorize the equation.
[tex]\Rightarrow x^{2} -12x+7x-84=0\\\Rightarrow x(x -12)+7(x-12)=0\\\Rightarrow (x+7)(x-12)=0\\\Rightarrow \bold{x=12, -7 }[/tex]
So, the numbers for which the given property hold true are 12 and -7.
