Question

what should be added to x²-3y²+2xy to obtain x²+y²+5xy​

Answer 1

Answer:

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Answer 2

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

Let us assume the term which should be added to x²-3y²+2xy be 'x'

According to the question:

=>x²-3y²+2xy + x=x²+y²+5xy

Now ,on the left side x²-3y²+2xy is positive when it moves to right side it gets substracted from x²+y²+5xy

=>x²-3y²+2xy +x =x²+y²+5xy

=>x=x²+y²+5xy-(x²-3y²+2xy)

=>x=x²+y²+5xy-x²+3y²-2xy

x² and -x² gets cancelled as both term having opposite sign.

=>x=x²-x²+y²+3y²+5xy-2xy

=>x=y²+3y²+5xy-2xy

=>x=4y²+5xy-2xy

=>x=4y²+3xy

Therefore,4y²+3xy should be added to x²-3y²+2xy to obtain x²+y²+5xy

Check:-

=>x²-3y²+2xy+4y²+3xy

=>x²-3y²+4y²+2xy+3xy

=>x²+y²+5xy

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