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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 5and2or -5and-2.

Step by step solution

01

Step 1. Given information.

Assume the two numbers to be xand y.

From the question,

x脳y=10......(i)x2-y2=21......(ii)

Solve equation (i) for x,

x=10y......(iii)

Substitute the value of x in equation (ii),

10y2-y2=21100y2-y2=21

02

Step 2. Find the two numbers.

Continuing the above equation,

100-y4-21y2=0y=卤2

Substitute y=2in equation (iii),

x=102x=5

Substitute y=-2in equation (iii),

x=10-2x=-5

Therefore, the numbers are 5and2or role="math" localid="1646837934125" -5and-2.

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