Chapter 11: Q. 73 (page 774)

The product of two numbers is $4$ , and the sum of their squares is $8$ . Find the numbers.

Short Answer

Expert verified

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

Step by step solution

Step 1. Given information.

Assume the two numbers to be xandy.

From the question,

$x \times y = 4 . . . . . . (i) x^{2} + y^{2} = 8 . . . . . . (i i)$

Solve equation (i) for x,

$x = \frac{4}{y} . . . . . . (i i i)$

Step 2. Substitute values in equation (ii).

Substitute the value of x in equation (ii),

${(\frac{4}{y})}^{2} + y^{2} = 8 \frac{16}{y^{2}} + y^{2} = 8 \frac{16}{y^{2}} + y^{2} - 8 = 0 16 + y^{4} - 8 y^{2} = 0 {(y^{2} - 4)}^{2} = 0$

Step 3. Find the two numbers.

Take square root both the sides,

$\sqrt{{(y^{2} - 4)}^{2}} = 0 y^{2} - 4 = 0 y = \pm 2$

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

$x = \frac{4}{2} x = 2$

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

$x = \frac{4}{- 2} x = - 2$

Therefore, the numbers are $2 a n d 2$ or $- 2 a n d - 2$ .

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The product of two numbers is $4$ , and the sum of their squares is $8$ . Find the numbers.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute values in equation (ii).

Step 3. Find the two numbers.

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The product of two numbers is 4, and the sum of their squares is 8. Find the numbers.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Substitute values in equation (ii).

Step 3. Find the two numbers.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Probability and Statistics

Logic and Functions

Study anywhere. Anytime. Across all devices.

The product of two numbers is $4$ , and the sum of their squares is $8$ . Find the numbers.