Answer:
The solution set of given algebraic expression is x = 7 and x = 3
Step-by-step explanation:
Given as :
The polynomial expression are
y = - x² + 6 x + 16 ............1
y = - 4 x + 37 ............2
Now, Solving these two equation
putting the value of y from eq 2 into eq 1
So, - x² + 6 x + 16 = - 4 x + 37
Or, - x² + 6 x + 16 + 4 x - 37 = 0
Or, - x² + (6 + 4) x + (16 - 37) = 0
Or, - x² + 10 x - 21 = 0
Now, solving this quadratic equation by middle term break
i.e - x² + 7 x + 3 x - 21 = 0
Or, - x ( x - 7) + 3 ( x - 7) = 0
Or, (x - 7) ( - x + 3) = 0
Or, (x - 7) = 0 and ( - x + 3 ) = 0
∴ x = 7 , x = 3
So, The solution set of given algebraic expression is x = 7 , x = 3
Hence, The solution set of given algebraic expression is x = 7 and x = 3 Answer
