SOLUTION: A positive real number is 4 more than another. If the sum of the squares of the two numbers is 72, find the numbers. (If applicable, write your answers in the form p±qsqrt(

Algebra ->  Rectangles -> SOLUTION: A positive real number is 4 more than another. If the sum of the squares of the two numbers is 72, find the numbers. (If applicable, write your answers in the form p±qsqrt(      Log On


   

Question 1091663: A positive real number is 4 more than another. If the sum of the squares of the two numbers is 72, find the numbers.
(If applicable, write your answers in the form p±qsqrt(r))
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
let one number be p and another number q
if one number is 4 more than another, we have:
p=q%2B4 ....eq.1
if the sum of the squares of the two numbers is 72, we have:
p%5E2%2Bq%5E2=72....eq.2....substitute p from eq.1
%28q%2B4%29%5E2%2Bq%5E2=72.....solve for q
q%5E2%2B8q%2B16%2Bq%5E2=72
2q%5E2%2B8q%2B16-72=0
2q%5E2%2B8q-56=0...simplify, divide by 2
q%5E2%2B4q-28=0

q+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
q+=+%28-4+%2B-+sqrt%28+4%5E2-4%2A1%2A%28-28%29+%29%29%2F%282%2A1%29+
q+=+%28-4+%2B-+sqrt%28+16%2B112+%29%29%2F2
q+=+%28-4+%2B-+sqrt%28+16%2A4%2A2+%29%29%2F2
q+=+%28-4+%2B-+%284%2A2%29sqrt%282%29%29%2F2
q=+%28-cross%284%292+%2B-+%284%2Across%282%29%29sqrt%282+%29%29%2Fcross%282%29
highlight%28q+=+%28-2+%2B-+4%2Asqrt%282%29%29%29
find p
p=q%2B4 ....eq.1
p=%28-2+%2B-+4sqrt%282%29%29%2B4
p=%284-2+%2B-+4sqrt%282%29%29
highlight%28p=%282+%2B-+4sqrt%282+%29%29%29