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Chapter 11: Q. 11.77 (page 1069)

The difference of the squares of two numbers is -20. The sum of the numbers is 10. Find the numbers.

Short Answer

Expert verified

The numbers are 4, 6.

Step by step solution

01

Step 1. Given information

  • The difference of the squares of two numbers is 鈭�20.
  • The sum of the numbers is 10.
02

Step 2. Form Equations

  • Assume that the numbers are x,y.
  • Their sum is 10. So, x+y=10.
  • Difference of their square is-20. So,role="math" localid="1645521245803" x2-y2=-20.
03

Step 3. Substitute value from one equation to other

  • Simplify the first equation for x.

x=10-y

  • Substitute this value into the second equation and solve for y.

(10-y)2-y2=-20-20y+100+20=0-10y+60=0y=6

04

Step 4. Solve for x

  • Substitute y=6into x+y=10and solve.

localid="1667920402220" x+6=10x=4

  • So, the numbers are 4, 6.

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Most popular questions from this chapter

In the following exercises, convert each number to decimal form.

(a) -8.3脳102 (b)3.8脳10-2

Solve the exercise

16y2+12=-32x

Factora2-11ab+10b2

For the functionf(x)=25x2-81, find:
(a) the zeros of the function.

(b) the x-intercepts of the graph

of the function.
(c) the y-intercept of the graph of the

function.

Simplify:

(a)2723

(b)81-32

(c)16-34
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