MHB Find the value of x square + y square

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To find the value of x² + y² given x - y = 1 and x²y - xy² = 2, the second equation can be factored to xy(x - y) = 2. Substituting x - y = 1 into this equation yields xy = 2. Using the identity x² + y² = (x - y)² + 2xy, we can calculate x² + y² as (1)² + 2(2), resulting in a final value of 5. The solution demonstrates the effective use of algebraic manipulation to derive the answer.
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If x-y= 1 & x2y - xy2 =2, Find the value of x2+y2

Any Ideas on how to begin?

Many Thanks :)
 
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mathlearn said:
If x-y= 1 & x2y - xy2 =2, Find the value of x2+y2

Any Ideas on how to begin?

Many Thanks :)

you can factor 2nd equation to get xy(x-y) = 2.
now put from 1st equation value of x-y to get xy * 1 = 2 or xy =2

now $(x^2+y^2) = (x-y)^2 + 2xy = 1 ^2 + 2 * 2 = 5$
 
kaliprasad said:
you can factor 2nd equation to get xy(x-y) = 2.
now put from 1st equation value of x-y to get xy * 1 = 2 or xy =2

now $(x^2+y^2) = (x-y)^2 + 2xy = 1 ^2 + 2 * 2 = 5$

Many Thanks :)
 

Thread 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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