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Chapter 11: Q. 232 (page 1148)

The difference of the squares of two numbers is 15. The difference of twice the square of the first number and the square of the second number is 30. Find the numbers.

Short Answer

Expert verified

3.873 and 0 or -3.873 and 0

Step by step solution

01

Step 1. Given information.

The difference between the squares of the two numbers is 15. Also, the difference between twice the square of the first number and the square of the second number is 30.

02

Step 2. Forming the equations. 

Let xbe the first number and ybe the second number.

From the given conditions, we can form the following equations:

x2-y2=15--->(1)2x2-y2=30--->(2)

03

Step 3. Solving the equations. 

Solving equation (1) for x2gives

x2=15+y2

Substituting this in equation (2):

215+y2-y2=3030+2y2-y2=30y2=0

Solving for y, we get that

y=0

From equation (1)

x2=15-0x=卤15x=卤3.873

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