Question

Find two numbers whose sum and product are 20 and 96 respectively

Answer 1

Answer:

The Numbers Are 12 and 8

12+8= 20

12*8= 96

Answer 2

Step-by-step-Explanation:

Given: Two numbers whose sum and product are 20 and 96 respectively.

To find: Find the two numbers.

Solution:

Let the two numbers are x and y.

Step 1: Write equations.

According to the given conditions write equations.

$x + y = 20...eq1$

$xy = 96...eq2$

Step 2: Put value of y from eq2 and eq1

$y = \frac{96}{x}$

$x + \frac{96}{x} = 20$

or

$\frac{ {x}^{2} + 96 }{x} = 20$

or

${x}^{2} + 96 = 20x$

or

${x}^{2} - 20x + 96 = 0$

Step 3: Solve the quadratic equation.

${x}^{2} - 12x - 8x + 96 = 0$

$x(x - 12) - 8(x - 12) = 0$

$(x - 12)(x - 8) = 0$

$x - 12 = 0$

$x = 12$

or

$x - 8 = 0$

$x = 8$

Step 4: Write the numbers.

When

$x = 12$

$12 + y = 20$

$y = 8$

When

$x = 8$

$8 + y = 20$

$y = 12$

Final answer:

Two numbers are 12 and 8.

Hope it helps you.

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