Question

If 2 X + 6 Y is equal to 60 and X Y is equal to 1 find X square + 9 y square

Answer 1

If x2+y2=29x2+y2=29, and even if you know x=5x=5, it is not sufficient to solve for yy, since the first equation is quadratic and you will get two answers for yy, namely 24−−√24 and −24−−√−24. So its impossible to know the sign of y, and hence the sign of xy. This is why (2) is not sufficient

 Kudos

 1

Answer 2

2x + 6y=60
2(x+3y)=60
x+3y=30

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(x+3y)^2=30^2
x^2+6xy+9y^2=900
x^2+6(1)+9y^2=900

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so,
x^2+6+9y^2=900
x^2+9y^2=900-6
x^2+9y^2=894


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SO THE ANSWER IS .......


x^2+9y^2=894


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