113k views
5 votes
Find two numbers which can multiply to get 2and when added to get 4

User Hopobcn
by
7.7k points

1 Answer

1 vote

Final answer:

The two numbers that multiply to get 2 and add up to get 4 are ±2 + √2 and 2 - √2, found by forming and solving a quadratic equation with the given sum and product as the coefficients.

Step-by-step explanation:

The problem is to find two numbers that multiply to get 2 and, when added, they equal 4. To find these two numbers, we can set up a system of equations based on the conditions given:

  • Let the two numbers be x and y.
  • The first condition can be represented as x × y = 2 (they multiply to 2).
  • The second condition is represented as x + y = 4 (they add up to 4).

To solve this system, we can use substitution or elimination. An alternative intuitive method is to recognize the conditions resemble the factoring of a quadratic equation's solutions. Since the sum and product of the roots of a quadratic equation ax² + bx + c = 0 are −b/a and c/a respectively, we can form the quadratic equation x² - (sum of numbers)x + (product of numbers) = 0. With the given conditions, this becomes x² - 4x + 2 = 0. Using the quadratic formula to solve for x gives us the two numbers:

x = [-(-4) ± √{{(-4)² - 4 × 1 × 2}}] / (2 × 1)
x = [4 ± √{(16 - 8)}] / 2
x = [4 ± √{8}] / 2
x = [4 ± √{4×2}] / 2
x = [4 ± 2√{2}] / 2
x = 2 ± √{2}

Therefore, the two numbers we are looking for are 2 + √{2} and 2 - √{2}.

User Ali Nobari
by
8.7k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories