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 :)
 

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