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If x and y are positive integers such th...

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

Text Solution

Verified by Experts

`:'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`
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