90.
2) √(4-0,5х)=2
4-0,5х=2²
-0,5х=4-4
-0,5х=0
х=0
Проверка:
√(4-0,5*0)=2
√4=2
2=2
Ответ: 0.
92. 1/3 и √0,1 (>)
√1 и √1
√9 √10
1 и 1
√9 √10
1 > 1
√9 √10
94.
2) √(3/5) * √(5 ²/₅) = √(3/5) * √(27/5) = √3 * √27 = √81 = 9/5 =1.8
√5 * √5 5
4) 2√8 = 2√8 = 2√8 = 2 = 2/7
√392 √(8*49) √8 * √49 √49
6) √(-4)⁶ = |-4|³ =64
96.
2) 2√(1/6) - √(2/3) +3√(1/15) +4√(3/5) =
= 2 - √2 + 3 + 4√3 =
√6 √3 √15 √5
= 2 - √2 + 3 + 4√3 =
√3 * √2 √3 √3 * √5 √5
=2√5 -√2 * √2 * √5 + 3√2 +4√3 * √3 * √2 =
√3 * √5 * √2
=2√5 - 2√5 +3√2 +12√2 = 15√2 = 15 = 15√15 =
√3 * √5 * √2 √15 * √2 √15 √15 * √15
=15√15 = √15
15
4) (1-√3)²(1+√3)=(1-√3)(1-√3)(1+√3)=(1-√3)(1-3)=-2(1-√3)=2√3 - 2
6) 2 + 3 = 2(3-√5) +3(1+√3) = 6-2√5 +3 +3√3 = 9 -2√5 +3√3
1+√3 3-√5 (1+√3)(3-√5) (1+√3)(3 -√5) (1+√3)(3-√5)
97.
2) 5√2 и 7 (>)
√(25*2) и √49
√50 и √49
√50 > √49
4) 3√5 и 2√7 (>)
√(9*5) и √(4*7)
√45 и √28
√45 > √28
98.
2) √(0.5a+5)
0.5a+5≥0
0.5a≥-5
a≥ -5 : 0,5
a≥ -10
a∈[-10; +∞)
4) √(-1/2 -3а)
-1/2 - 3а ≥0
-3а≥1/2
а≤ 1/2 : (-3)
а≤ -1/6
а∈(-∞; -1/6]
99.
2) b≤0
√(2/9)b² = -b√2
3
4) a<0, b>0
√0.32a²b³ = -0.4ab√(2b)
6) a≥0, b≤0
√(1/9)a⁵b⁶ = -1/3 a²b³√a
100.
2) x<0<br>x√2 = -√(2x²)
4) a≥0
-a√3 = -√(3a²)
101.
2) 4√5 = 4√5 * √6 =4√30 = 2√30
√6 √6 * √6 6 3
4) √11 + √3 = (√11 +√3)(√3 +√11) = 11 +2√33 +3 = 14 +2√33 =
√3 - √11 (√3 - √11)(√3 +√11) 3-11 -8
= 2(7+√33) = -7-√33
-8 4