SOLUTION: Find two numbers such that the smaller subtracted from the larger is 3 and the difference of the square of the larger subtracted from square of the smaller is 45.
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Question 1118976: Find two numbers such that the smaller subtracted from the larger is 3 and the difference of the square of the larger subtracted from square of the smaller is 45. Found 2 solutions by josgarithmetic, ikleyn:Answer by josgarithmetic(39616) (Show Source):
You can put this solution on YOUR website! .
Find two numbers such that the smaller subtracted from the larger is 3 and
the difference of the square of the larger subtracted from square of the smaller is 45.
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You are given
x - y = 3 (1) (where x is the larger number)
y^2 - x^2 = 45. (2)
From eq(2), you have
(y-x)*(x+y) = 45.
Replace (y-x) in the left side by -3, based on eq(1). You will get
-3*(x+y) = 45, or
x + y = -45/3 = -15.
Thus you have two equatiuons
x - y = 3, (1)
x + y = -15 (3) <<<---=== you were fortune to reduce the given system with a quadratic equation to system of two linear equations !
Add them to get 2x = 3+(-15) = -12 ====> x = -12/2 = -6.
Then from eq(1), y = x - 3 = -6-3 = -9.
Answer. The numbers are -6 and -9.
Check. (-9)^2 - (-6)^2 = 81 - 36 = 45. ! Correct !
Solved.
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Be aware: the answer by @josgarithmetic "6 and 9" is INCORRECT !