Verified answer

To solve for x⁴ + ¼ using the given equations:

(i) x + 1/x = 3

(ii) x - 1/x = 4

We can use the given equations to find x² and x⁴, and then substitute them into x⁴ + ¼ to solve for the value of the expression.

Adding equations (i) and (ii), we get:

2x = 7

Solving for x, we get:

x = 7/2

Subtracting equation (ii) from equation (i), we get:

2/x = -1

Solving for x, we get:

x = -2

However, this value of x does not satisfy equation (i), so we must discard it.

Therefore, we have:

x = 7/2

Now we can use x to find x²:

x² = (x + 1/x)² - 2

x² = 3² - 2

x² = 7

Next, we can use x² to find x⁴:

x⁴ = (x²)²

x⁴ = 7²

x⁴ = 49

Finally, we can substitute x⁴ = 49 into x⁴ + ¼:

x⁴ + ¼ = 49 + ¼

x⁴ + ¼ = 49.25

Therefore, the value of x⁴ + ¼ is 49.25.

~ I hope this helps Cutiepie ❤️!

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