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Chapter 11: Q. 231 (page 1148)

The sum of the squares of two numbers is 113. The difference of the number is 1. Find the numbers.

Short Answer

Expert verified

-7 and -8 or 8 and 7

Step by step solution

01

Step 1. Given information.

The sum of the squares of two numbers is 113 and the difference between the two numbers is 1.

02

Step 2. Forming the equations. 

Letxbe the first number andybe the second number.

From the condition that the sum of the squares of the two numbers is 113, we get the following equation:

x2+y2=113--->(1)

From the condition that the difference of the two numbers is 1, we get the following equation:

x-y=1--->(2)

03

Step 3. Solving the equations. 

Solving equation (2) for xgives

x=y+1

Substituting this in equation (1) gives

y+12+y2=113y2+2y+1+y2=1132y2+2y-112=0--->(3)

Dividing both sides by 2 gives

y2+y-56=0

Factorising the quadratic equation gives

y2+8y-7y-56=0y+8y-7=0

If y+8=0, then y=-8and x=1+y=1+(-8)=-7

Ify-7=0, theny=7andx=1+y=1+7=8

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