Question

Va rog sa ma ajutati sa rezolv exercitiile din imagine.Va multumesc.

Answer 1

12/(3√2-2√3) +18/(2√3-3) - 14/(4√2-5)=
=12(3√2+2√3)/(3√2-2√3) (3√2+2√3)  +18(2√3+3)/(2√3-3)(2√3+3) - 14(4√2+5)/(4√2-5)(4√2+5)=12(3√2+2√3)/(9*2-4*3)  +18(2√3+3)/(4*3-9) - 14(4√2+5)/(16*2-25)=
=12(3√2+2√3)/6  +18(2√3+3)/3 - 14(4√2+5)/7=
=2(3√2+2√3)  +6(2√3+3) - 2(4√2+5)=
=6√2+4√3+12√3+18-8√2-10=16√3-2√2+8 

8/(2√5-4)+2√5/(√5+2)-4√5/(7-3√5)=
=8(2√5+4)/(2√5-4)(2√5+4)+2√5(√5-2)/(√5+2)(√5-2)-4√5(7+3√5)/(7-3√5)(7+3√5)=
=8(2√5+4)/(20-16)+2√5(√5-2)/(5-4)-4√5(7+3√5)/(49-45)=
=8(2√5+4)/4+2√5(√5-2)-4√5(7+3√5)/4=
=2(2√5+4)+2√5(√5-2)-√5(7+3√5)=
=4√5+8+10-4√5-7√5-15=
=3-7√5

Answer 2

2/(3√2-2√3) +18/(2√3-3)-14/(4√2-5)
=12(3√2+2√3)/(3√2-2√3) (3√2+2√3)+18(2√3+3)/(2√3-3)(2√3+3) - 14(4√2+5)/(4√2-5)(4√2+5)=12(3√2+2√3)/(9*2-4*3)+18(2√3+3)/(4*3-9)-14(4√2+5)/(16*2-25)
=12(3√2+2√3)/6+18(2√3+3)/3 - 14(4√2+5)/7
=2(3√2+2√3)+6(2√3+3)-2(4√2+5)
=6√2+4√3+12√3+18-8√2-10=16√3-2√2+8
8/(2√5-4)+2√5/(√5+2)-4√5/(7-3√5)
=8(2√5+4)/(2√5-4)(2√5+4)+2√5(√5-2)/(√5+2)(√5-2)-4√5(7+3√5)/(7-3√5)(7+3√5)
=8(2√5+4)/(20-16)+2√5(√5-2)/(5-4)-4√5(7+3√5)
=8(2√5+4)/4+2√5(√5-2)-4√5(7+3√5)/4
=2(2√5+4)+2√5(√5-2)-√5(7+3√5)
=4√5+8+10-4√5-7√5-15= ....
=3-7√5