Question

What is the solution(s) to f(x) = g(x), where f(x) = x^2−2 and g(x) = 5x − 8

Answer 1

If f(x)=g(x), than x²-2=5x-8

Now we need to solve this equation

$x^2-2=5x-8\\x^2-5x+6=0\\D=b^2-4ac=(-5)^2-4\times6=25-24=1=\sqrt{1} ^2\\x_1=\dfrac{5+1}{2}=3\\ x_2=\dfrac{5-1}{2} =2$

Answer: 2, 3