SOLUTION: Find two numbers such that the smaller subtracted from the larger is 9 and the difference of the square of the larger subtracted from square of the smaller is 9.

Algebra.Com
Question 1118978: Find two numbers such that the smaller subtracted from the larger is 9 and the difference of the square of the larger subtracted from square of the smaller is 9.
Found 3 solutions by josgarithmetic, greenestamps, ikleyn:
Answer by josgarithmetic(39617)   (Show Source): You can put this solution on YOUR website!
**






Equivalent system should be
and may be easier to solve.

Elimination Method should give

** The above solution may be mistaken. Description states, "the difference of the square of the larger subtracted from square of the smaller is 9. "; which should mean, and .
Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!


Let a be the larger number and b the smaller. Then

(1)
(2)

Dividing (2) by (1) gives

(3)

Then (1) and (2) with a little algebra give the answer:

a = 5; b = -4

If you are good with mental arithmetic, you might realize that the only time the squares of two integers differ by 9 is with . So the absolute values of the two numbers are 5 and 4; then to get a difference of 9 between the two numbers, you get the answers 5 and -4.

-----------------------------------------------
Tutor @ikleyn is right; I didn't read the question carefully enough.

Since it is the smaller subtracted from the larger that gives a result of 9, the numbers are 4 and -5; not 5 and -4.
Answer by ikleyn(52777)   (Show Source): You can put this solution on YOUR website!
.
Find two numbers such that the smaller subtracted from the larger is 9 and
the difference of the square of the larger subtracted from square of the smaller is 9.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~


            The correct answer is  4  and  -5.

            Both @greenestamps and @josgarithmetic produced wrong solutions and wrong answers. 


You are gven that

a - b = 9         (1)     (where "a" is the larger number)
b^2 - a^2 = 9     (2)


From eq(2), you have  

(b-a)*(a+b) = 9.   (3)


In (3), replace (b-a) by -9, since it is given (see (1) ). You will get

(-9)*(a+b) = 9,   or

a + b = -1.


Thus you have this system of two linear equations

a - b =  9,   (1)
a + b = -1    (4)


Add them. You will get

2a = 9 + (-1) = 8  ====>  a = 8/2 = 4.


Then from eq(4),  b = -1 - 4 = -5.


Check.    b^2 - a^2 = (-5)^2 - 4^2 = 25 - 16 = 9.   ! Correct !


RELATED QUESTIONS

Find two numbers such that the smaller subtracted from the larger is 3 and the difference (answered by josgarithmetic,ikleyn)
The larger of two numbers is 9 less than 6 times the smaller number, when the smaller... (answered by rfer)
The larger of two numbers is 9 less than seven times the smaller when the smaller number... (answered by josgarithmetic,addingup)
The larger of two numbers is 9 less than eight times the smaller. When the smaller number (answered by jorel555)
Find two consecutive even intergers such that the smaller interger subtracted from twice... (answered by solver91311)
the larger of two integers is five halves the smaller. if twice the smaller is subtracted (answered by TimothyLamb)
The sum of two numbers is 48. If the smaller number is subtracted from the larger, the... (answered by richwmiller)
the sum of two numbers is 73 The difference when the smaller number is subtracted from... (answered by tommyt3rd,richwmiller)
The larger of two numbers is 5 more than twice the smaller. If the smaller is subtracted... (answered by JulietG)