If x2+y2=34 and xy=10 1/2 then find 2(x+y)^2+(x-y)^2

If x2+y2=34 and xy=10 1/2 then find 2(x+y)^2+(x-y)^2[ ICSE Class 9 S.Chand (Fundamentals of Mathematics) Chapter 3 Exercise-3.1 Question Number 16 Solution Expansion and Factorisation]

2(x+y)²+(x-y)²

= 2(x²+2xy+y²)+(x²-2xy+y²)

=2(x²+y²+2xy)+(x²+y²-2xy)

=2(x²+y²) +4xy+ (x²+y²) -2xy

= 3(x²+y²)+2xy

= 3×34 +2 × $10\frac{1}{2}$

= 102 + 2 × $\frac{21}{2}$

=102 +21

= 123

Therefore 2(x+y)²+(x-y)² = 123