Given the two equations:

(i) $ 2x^3 = \sqrt{256} $

(ii) $ 2y^2 - 9y + 10 = 0 $

Find the correct relationship between $ x $ and $ y $.

Question

Given the two equations:

(i) $ 2x^3 = \sqrt{256} $

(ii) $ 2y^2 - 9y + 10 = 0 $

Find the correct relationship between $ x $ and $ y $.

Accepted Answer

**Solution:**

1. Solve equation (i):

$$
2x^3 = \sqrt{256}
$$

Since $ \sqrt{256} = 16 $, the equation becomes:

$$
2x^3 = 16 \implies x^3 = 8 \implies x = 2
$$

2. Solve equation (ii):

$$
2y^2 - 9y + 10 = 0
$$

We factorize the quadratic:

$$
2y^2 - 5y - 4y + 10 = 0
$$

Group terms:

$$
y(2y - 5) - 2(2y - 5) = 0
$$

Factor out $ (2y - 5) $:

$$
(2y - 5)(y - 2) = 0
$$

So,

$$
y = 2 \quad \text{or} \quad y = \frac{5}{2} = 2.5
$$

3. Compare $ x $ and $ y $:

$$
x = 2, \quad y = 2 \text{ or } 2.5
$$

Since $ x = 2 $ and $ y $ can be either $ 2 $ or $ 2.5 $, the relationship is:

$$
x \leq y
$$

**Answer:** $ x≥y $ (Option (c))

Answer

Answer

Answer