find the difference between two positive numbers is 4 and the sum of their squares is 58. Find the numbers

the bigger number is=

the smaller number is =

Tutors, sign in to answer this question.

a-b=4

a^2+b^2=58

a-b=4 implies a=b+4

substitute

(b+4)^2+b^2=58

b^2+8b+16+b^2=58

2b^2+8b+16=58

2b^2+8b+16-58=0

2b^2+8b-42=0

b^2+4b-21=0

(b+7)(b-3)=0

b-3=0

b=3

a-3=4

a=7

a=7,b=3

don't forget, you said two positive numbers so we stop here

A-B=4 (1)

A²+B²=58 (2)

(A-B)²=A²-2AB+B²=16

Substitute from equation (2)

(A-B)²=-2AB+58=16

So now have -2AB+58=16 or that -2AB=-42 or that AB=21

Look at A-B=4 and AB=21

Substitute A=B+4 into AB=21 and have (B+4)B=21 or that

B²+4B-21=0 which factors int (B+7)(B-3)=0 which gives that B=3 or B=-7

For B=3, A=7 and A²+B²=58

For B=-7, A=-11 and A²+B²=170 not a solution

Smaller number =3; larger number =7

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.