Question

1)(1+√5-√3)(1-√5-√3)+(1-√7+√3)(1+√7+√3). 2) -5\6-1\6•+2\3) la puterea -2. 3)√1225. 4)|2x-3|=5. 4)5√3. 5) a^2-b^2=45 a-b=15 5a-5b

Answer 1

1)(1+√5-√3)(1-√5-√3)+(1-√7+√3)(1+√7+√3)=1-√5-√3+√5-5-√15-√3+√15+3+1+√7+√3-√7-7-√21+√3+√21+3=
1-5+3+1-7+3-√5+√5-√3-√3+√3+√3-√15+√15+√7-√7-√21+√21=-4

 2) -5/6-1/6•(+2/3)²=-6/6·4/9=-4/9=-0,(4)

 3)√1225=√(5²·7²)=5·7=35

4)|2x-3|=5cazul 1:  2x-3=5
2x=5+3
x=8/2
x=4
cazul 2:  2x-3=-5
2x=-5+3
2x=-2
x=-2/2
x=-1
S={-1,4}

4)5√3=√(5²·3)=√75

5) a²-b²=45 
a-b=15  ⇒a=15+b
inlocuim in relatia a²-b²=45(15+b)²-b²=45
225+30b+b²-b²=45
225+30b=45
30b=45-225
b=-180/30
b=-6
din relatia a-b=15
avem a-(-6)=15
a+6=15
a=15-6
a=9
5a-5b=5(a-b)=5[9-(-6)]=5(9+6)=5·15=90