Chapter 11: Q. 74 (page 774)

The product of two numbers is $10$ , and the difference of their squares is $21$ . Find the numbers.

Short Answer

Expert verified

The two numbers are $5 a n d 2$ or $- 5 a n d - 2$ .

Step by step solution

Step 1. Given information.

Assume the two numbers to be xand y.

From the question,

$x \times y = 10 . . . . . . (i) x^{2} - y^{2} = 21 . . . . . . (i i)$

Solve equation (i) for x,

$x = \frac{10}{y} . . . . . . (i i i)$

Substitute the value of x in equation (ii),

${(\frac{10}{y})}^{2} - y^{2} = 21 \frac{100}{y^{2}} - y^{2} = 21$

Step 2. Find the two numbers.

Continuing the above equation,

$100 - y^{4} - 21 y^{2} = 0 y = \pm 2$

Substitute $y = 2$ in equation (iii),

$x = \frac{10}{2} x = 5$

Substitute $y = - 2$ in equation (iii),

$x = \frac{10}{- 2} x = - 5$

Therefore, the numbers are $5 a n d 2$ or role="math" localid="1646837934125" $- 5 a n d - 2$ .

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The product of two numbers is $10$ , and the difference of their squares is $21$ . Find the numbers.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the two numbers.

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The product of two numbers is 10, and the difference of their squares is 21. Find the numbers.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the two numbers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Geometry

Applied Mathematics

Statistics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

The product of two numbers is $10$ , and the difference of their squares is $21$ . Find the numbers.