SOLUTION: (1)ONE NUMBER EXCEEDS ANOTHER BY 5 THE SUM OF THEIR SQUARES IS 120,FIND THE NUMBERS. (2)TWO NUMBERS DIFFERS BY 6,THE DIFFERENCE OF THEIR SQUARES IS 120,FIND THE

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Question 1178016: (1)ONE NUMBER EXCEEDS ANOTHER BY 5 THE SUM OF THEIR SQUARES IS 120,FIND THE NUMBERS. (2)TWO NUMBERS DIFFERS BY 6,THE DIFFERENCE OF THEIR SQUARES IS 120,FIND THE NUMBERS.
Found 2 solutions by mananth, MathLover1:
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let one number be x
other number will be x+5
x^2+(x+5)^2= 120
x^2+x^2+10x +25=120
2x^2 +10x -95=0
x= -9.8 or 4.8

x , x+6
x^2-(x+6)^2 =120
x^2-x^2-12x -36 =120
-12x 156
x=-13
-13, -18

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

(1)ONE NUMBER EXCEEDS ANOTHER BY 5 THE SUM OF THEIR SQUARES IS 120,FIND THE NUMBERS.
let first number be x
and second number y
if second number exceeds first by 5
so, we have x=y-5..........eq.1
the sum of their squares is 120
x%5E2%2By%5E2=120
%28y-5%29%5E2%2By%5E2=120
2+y%5E2+-+10+y+%2B+25=120
2+y%5E2+-+10+y+%2B+25-120=0
2+y%5E2+-+10+y+-95=0...........using quadratic formula we get
y+=+5%2F2+%2B+sqrt%28215%29%2F2 or y=9.83143914930759
or
y+=+5%2F2+-+sqrt%28215%29%2F2 or y=-4.83143914930759
then
x=5%2F2+%2B+sqrt%28215%29%2F2-5 or x=4.83143914930759
or
x=5%2F2+-sqrt%28215%29%2F2-5 or x=-9.83143914930759
your numbers are:
4.83143914930759 and 9.83143914930759
or
-4.83143914930759 and -9.83143914930759
check: for accuracy using all decimal places
9.83143914930759%5E2%2B%28-4.83143914930759%29%5E2=120
120=120

(2)TWO NUMBERS DIFFERS BY 6,THE DIFFERENCE OF THEIR SQUARES IS 120,FIND THE NUMBERS.
let first number be x
and second number y
if second number differ by 6
so, we have y=x-6..........eq.1
the difference of their squares is 120
x%5E2-y%5E2=120
x%5E2-%28x-6%29%5E2=120
x%5E2-%28x%5E2-12x%2B36%29=120
x%5E2-x%5E2%2B12x-36=120
12x-36=120.........simplify, divide by 12
x-3=10
x=10%2B3
x=13
then
y=x-6->y=13-6->y=7
your numbers are: 13 and 7
check the difference of their squares:
13%5E2-7%5E2=120
169-49=120
120=120