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The product of two numbers is 10 and the difference of their squares is 21. Find the numbers.

          The product of two numbers is 10 and the difference of their squares is 21. Find the numbers.
        

Added by Travis R.

Precalculus with Limits
Precalculus with Limits
Ron Larson 2nd Edition
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The product of two numbers is 10 and the difference of their squares is 21. Find the numbers.
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Transcript

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00:01 Okay, here we have two numbers.
00:02 Let's call them x and y.
00:04 So their product, x times y, is 10.
00:10 And difference of their squares.
00:12 So x squared minus y squared, which is 21.
00:18 So first step then translate from the words into two equations.
00:23 Now, from here, i can see that y is 10 divided by x, which means here i can.
00:32 Can replace the y by 10 divided by x and get that result, which means we have x squared minus 100 over x squared equals 21.
00:51 Now times both sides by x squared and get x to the fourth minus 100 is 21 x squared.
01:02 We arrange that x to the fourth minus 21 x squared...
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