Question

решите плиз:
1)$( sqrt{x}- sqrt{y})^{2}+( sqrt{x}+ sqrt{y})^{2}$
2)($2 sqrt{a}+3 sqrt{b})^{2}+(2 sqrt{a}+3 sqrt{b})(2 sqrt{a}-3 sqrt{b})$

Answer 1

1)$( sqrt{x} - sqrt{y} )^2+( sqrt{x} + sqrt{y} )^2$
$( sqrt{x} )^2-2 sqrt{xy} +( sqrt{y} )^2+( sqrt{x} )^2+2 sqrt{xy}+( sqrt{y} )^2$
$x+y+x+y=2x+2y=2(x+y)$
2)$(2 sqrt{a}+3 sqrt{b} )^2+(2 sqrt{a}+3 sqrt{b})(2 sqrt{a}-3 sqrt{b})$
$(2 sqrt{a} )^2+2*2*3 sqrt{ab}+(3 sqrt{b} )^2 +(2 sqrt{a} )^2-6 sqrt{ab}+6 sqrt{ab}-(3 sqrt{b})^2$
$4a+12 sqrt{ab}+9b+4a-9b$
$8a+12 sqrt{ab}$

Answer 2

$(2sqrt{a}+3sqrt{b})^2+(2sqrt{a}+3sqrt{b})(2sqrt{a}-3sqrt{b})=\ (2sqrt{a}+3sqrt{b})^2+(4a-9b)=\ 4a+9b+12sqrt{ab}+4a-9b=8a+12sqrt{ab}$

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