Hey! to all MATHEMATICIANS out there! What is the solution and answer to this question?

Question

Find two numbers whose difference is 5 and the difference of their squares is 65.

Please answer this using the ff. methods:
Defining the variables;
Thought processes;
equation; and
final anwer.

You can use the ff. to solve this:
Square root property;
factoring;
completing the square; or
quadratic formula.

This is about PROBLEM SOLVING INVOLVING QUADRATIC FORMULA.

The variable is only ONE.

THANKS FOR ANSWERING!!!

Answer 1

4 AND 9

Let the numbers be x and (x+5), since the difference of the numbers is 5.

the difference of the squares are 65,
therefore, (x+5)² - x² = 65

Expanding it gives:
x²+10x+25-x² = 65
10x +25 = 65
10x = 40
x = 4

Answer 2

Let the numbers be x and (x+5), since the difference of the numbers is 5.

the difference of the squares are 65,
therefore, (x+5)² - x² = 65

Expanding it gives:
x²+10x+25-x² = 65
10x +25 = 65
10x = 40
x = 4

therefore, the numbers are 4 and 9

Answer 3

If X-Y = 5
then X = 5+Y
and If X^2-Y^2=65
Then (5+Y)^2 -Y^2 = 65
therefore 25 +10Y +Y^2-Y^2=65
therefore 10Y=40
Y=4 & X = 5+4=9

Answer 4

X^2-Y^2 = 65
take the difference of two squares;
(x+y)(x-y) =65
now x-y =5
x+y = 65/5 =13
add the two simultaneous equation ;
y cancel out ,x = 9
Y=4

Answer 5

By trial and error, the answer is: 9 and 4
81-16=65

Answer 6

This 1 is linear.

a-b=5
a^2-B^2=65a=b+5
(b+5)^2-b^2=65
b^2+10b+25-b^2=65
10b=65-25=40

b=4

a=b+5=4+5=9

check

9^2-4^2=92-16=65

Answer 7

x - y = 5

x exp2 - y exp2 = 65

______________________


y = x - 5

putting this in the second formula:

x exp2 - ( x - 5 ) exp2 = 65

x exp2 - ( x exp2 - 10* x + 25) =65

x exp2 - x exp2 + 10*x - 25 = 65

10*x = 65 + 25

x = 90 / 10

x = 9
-------------- and

y = x - 5

y = 4

___________________


Verification:


9 - 4 = 5 o.k.

9 exp2 - 4 exp2 = 81 - 16 = 65 o.k.

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any other question??

Answer 8

I full y agree with CANZONI and his method of application to solve the problem. Bravo CANZONI.