Chapter 11: Q. 350 (page 1161)

The sum of two numbers is $22$ and the product is $- 240$ .Find the numbers.

Short Answer

Expert verified

The solution are Line and Hyperbola.

Step by step solution

Step 1. Given Information

Given that the two numbers is $22$ and product is $240$ .

Step 2. Standard form

The equation can be denoted as,

$x + y = 22 is linear xy = - 240 is non - linear$

That is hyperbola equation.

Step 3. Standard equation

It can be denoted as,

$x + y - 22 = 0 xy = - 240 x = \frac{- 240}{x}$

The standard form of $x + y = 22 is x + y - 22 = 0 and xy = - 240 is x = \frac{- 240}{x} .$

Step 4. Number of equation

Let the first and second number are x and y. On solving the equation,

$x + y = 22 y = 22 - x xy = - 240 x (22 - x) = - 240 22 x - x^{2} = - 240 x^{2} - 22 - 240 = 0 a = 1, b = - 22, c = - 240 x = \frac{- b \pm \sqrt{b^{2} - 4 ac}}{2 a} x = \frac{22 \pm \sqrt{{(- 22)}^{2} - 4 \times 1 \times - 240}}{2 \times 1} x = - 8, 30$

Step 5. Graph of the equation

The graph of linear and non linear equation can be drawn as,

Step 6. Intersection point

The hyperbola and line can be intersected at $(- 8, 30) and (30, - 8) .$ It can be verified as,

$x + y = 22 - 8 + 30 = 22 22 = 22 xy = - 240 (30) (- 8) = - 240 - 240 = - 240$

The point of intersection satisfied both the equation.

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The sum of two numbers is $22$ and the product is $- 240$ .Find the numbers.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Standard form

Step 3. Standard equation

Step 4. Number of equation

Step 5. Graph of the equation

Step 6. Intersection point

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The sum of two numbers is 22and the product is -240.Find the numbers.

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Standard form

Step 3. Standard equation

Step 4. Number of equation

Step 5. Graph of the equation

Step 6. Intersection point

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Logic and Functions

Discrete Mathematics

Probability and Statistics

Applied Mathematics

Decision Maths

Statistics

Study anywhere. Anytime. Across all devices.

The sum of two numbers is $22$ and the product is $- 240$ .Find the numbers.