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Could someone please show me how (\((x^8+25)^.5 \) is not equal to \(x^4 +5\)

 Apr 7, 2023
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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.

 Apr 7, 2023

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