Could someone please show me how (\((x^8+25)^.5 \) is not equal to \(x^4 +5\)
We can prove this by a counterexample.
Let's assume that √(x^8 + 25) = x^4 + 5
Squaring both sides of the equation, we get:
x^8 + 25 = (x^4 + 5)^2
Expanding the right side, we get:
x^8 + 25 = x^8 + 10x^4 + 25
Subtracting 25 from both sides, we get:
x^8 = 10x^4
Dividing both sides by x^4, we get:
x^4 = 10
But this is a contradiction because x can be any real number, and there is no value of x that satisfies x^4 = 10.
Therefore, our initial assumption is false, and we have shown that:
√(x^8 + 25) is not equal to x^4 + 5 for any value of x.