The product of the two numbers is equal to the product of their HCF and LCM, which is 15 * 150 = 2250.

If the HCF is equal to one of the numbers, it means that one number is a multiple of the other.

The other number can be found using the formula: LCM = (a * b) / HCF. Here, 120 = (30 * b) / HCF. Assuming HCF is 30, b = 120 / 30 = 40.

The product of the two numbers is LCM * HCF = 36 * 6 = 216.

The product of the two numbers is HCF * LCM = 5 * 60 = 300.

The other number can be found using the formula LCM(a, b) = (a * b) / HCF(a, b). Here, 72 = (8 * x) / HCF(8, x). The other number is 18.

The other number can be found using the formula: LCM = (a * b) / HCF. Here, 84 = (12 * b) / HCF. The other number is 28.

Using the sum of roots: p = -(3 + (-2)) = -1.

The sum of the roots is p = 3 + 4 = 7.

x/y = 2^(3)/2^(4) = 2^(3-4) = 2^(-1) = 1/2.

x^4 = (2^(3/4))^4 = 2^3 = 8.

x = √(25) = 5, thus x^2 = 5^2 = 25.

This is a perfect square: (x + 2)^2 = 0, so x = -2.

Factoring gives (x - 2)(x - 3) = 0, so x = 2 and x = 3.

Factoring gives (x - 3)(x + 3) = 0, so x = -3 or x = 3.

7 divided by 3 gives a remainder of 1.

Subtract 3 from both sides: 2x = 8. Then divide by 2: x = 4.

Add 12 to both sides: 3x^2 = 12. Divide by 3: x^2 = 4. Thus, x = ±2.

This factors to (2x - 3)(2x - 3) = 0, giving the double root x = 3.

Add 16 to both sides: 4x^2 = 16. Divide by 4: x^2 = 4. Thus, x = ±2.

Factoring gives 5x(x + 2) = 0, so x = 0 or x = -2.

This factors to (x + 3)(x + 3) = 0, so x = -3.

Subtract 4 from both sides: 3y = 15. Divide by 3: y = 5.

Factoring gives (x - 2)(x - 3) = 0, so x = 2 and x = 3.

Factoring gives (x + 4)(x - 2) = 0, so x = -4 and x = 2.

This factors to (x + 2)(x + 2) = 0, so the double root is x = -2.

The discriminant is b^2 - 4ac = 3^2 - 4(2)(1) = 9 - 8 = 1.

Discriminant D = b² - 4ac = (-4)² - 4(2)(2) = 16 - 16 = 0.

The discriminant is b^2 - 4ac = 6^2 - 4*3*2 = 36 - 24 = 12.

The HCF of 100 and 250 is 50, as it is the largest number that divides both.