Question

1÷x+1÷y=3 , xy+x+y=4 find x squre y+xy squre

Answer 1

$\frac{1}{x} +\frac{1}{y} = 3\\\\\frac{x+y}{xy} =3\\x+y=3xy---(1)$

$xy+x+y=4\\x+y=4-xy----(2)$

Since (1) = (2) = x + y,

3xy = 4 - xy

3xy + xy = 4

4xy = 4

xy = 1    ---------(3)

Substituting (3) in (1),

x + y = 3*1

x + y = 3

We need to find,

$x^{2} y+xy^{2} =xy(x+y)$

Substituting x + y = 3 and xy = 1 we get,

$x^{2} y+xy^{2} =xy(x+y) = 1*(3) = 3$

Hence, x²y + xy² = 3

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