Question

what should be added to x²+xy+y² to obtain 2x²+3xy?

Answer 1

Let "a" be added to x^2 + xy +y^2 to obtain 2x^2 + 3xy

So a = 2x^2 + 3xy - (x^2 + xy + y^2)
= 2x^2 + 3xy - x^2 -xy - y^2
= x^2 + 2xy - y^2.

So x^2 + 2xy - y^2 must be added.

Answer 2

Answer:

x²+2xy-y² should be added to x²+xy+y² to obtain 2x²+3xy

Explanation:

Let A = x²+xy+y²,

B = 2x²+3xy ,

Let m should be added to A to obtain B

Now ,

m + A = B

=> m = B - A

=> m = (2x²+3xy) - (x²+xy+y²)

= 2x²+3xy-x²-xy-y²

= 2x²-x²+3xy-xy-y²

= x²+2xy-y²

Therefore,

m = x²+2xy-y²

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