1.
9√a-2√(a^2x)-3√(b^2/a)-6√[(b^2x)/9]
=9√a-2√(a^2x)+3b√(1/a)+6b√(x/9)
=9√a-2√(a^2x)+3b√a+6b√(x/9)
=9√a-2√(a^2x)+3b√a+2b√x
=9√a-2a√x+3b√a+2b√x
=9√a+3b√a+2b√x-2a√x
=3√a(3+b)+2√x(b-a)
2.
a^2b-ab^2
=ab(a-b)
=(3+2√2)(3-2√2)[(3+2√2)-(3-2√2)]
=[(3+2√2)-(3-2√2)]
=3+2√2-3+2√2
=4√2
3.
√x+√y=√5-√3
√(xy)=√15-√3
x+y=(√x+√y)^2-2√(xy)
=(√5-√3)^2-2(√15-√3)
=(3+5-2√15)-2√15+2√3
=8-2√15-2√15+2√3
=8-4√15+2√3
4.
x=(2+√3)/(2-√3)
=(2+√3)^2/(2-√3)(2+√3)
=(2+√3)^2
=7+4√3
y=(2-√3)/(2+√3)
=(2-√3)^2/(2-√3)(2+√3)
=(2-√3)^2
=7+4√3
x-y=7+4√3-7+4√3=8√3
xy=(2-√3)/(2+√3)*(2+√3)/(2-√3)=1
2x^2-3xy+2y^2
=2x^2-4xy+2y^2+xy
=2(x^2-2xy+y^2)+xy
=2(x-y)^2+xy
=2(x-y)^2+1
=2*(8√3)^2+1
=2*192+1
=384+1
=385