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

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) (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) (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
and second number
if second number exceeds first by
so, we have ..........eq.1
the sum of their squares is

...........using quadratic formula we get
or
or
or
then
or
or
or
your numbers are:
and
or
and
check: for accuracy using all decimal places

(2)TWO NUMBERS DIFFERS BY 6,THE DIFFERENCE OF THEIR SQUARES IS 120,FIND THE NUMBERS.
let first number be
and second number
if second number differ by
so, we have ..........eq.1
the difference of their squares is

.........simplify, divide by

then
->->
your numbers are: and
check the difference of their squares:

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