If x and y are positive integers such that, `xy+x+y=71,x^2 y+xy^2=880, then x^2+y^2=`a)125 b)137 c)146 d)152

Options

A. 125
B. 137
C. 146
D. 152

Explanation

`:'xy+xy=71`impliesxy+x(x+y)=71`
and `x^(2)y+xy^(2)=880impliesxy(x+y)=880`
`impliesxy` and `(x+y)` are the roots of the quadratic equation.
`t^(2)-71t+880=0`
`implies(t-55)(5-16)=0`
`impliest=55,16`
`:.x+y=16` and `xy=55`
So `x^(2)+y^(2)=(x+y)^(2)-2xy=(16)^(2)-110=146`