Odpowiedź :
a) (7-4√3)(x+√3)=6
7x-4√3x+7√3-4√3*√3=6
x(7-4√3)+7√3-12=6
x(7-4√3)=6+12-7√3
x(7-4√3)=18-7√3 /*(7+4√3)
x(7-4√3)(7+4√3)=(18-7√3)(7+4√3)
x(7²-(4√3)²)=126+72√3-49√3-84
x(49-48)=42+23√3
x*1=42+23√3
x=42+23√3
b) x√7+3=x-5
x√7-x=-5-3
x(√7-1)=-8 /*(√7+1)
x(√7-1)(√7+1)=-8(√7+1)
x((√7)²-1²)=-8√7-8
x(7-1)=-8√7-8
6x=-8√7-8 /:6
x=(-8/6)√7-8/6
x=(-4/3)√7-4/3
c) x-2=x√3-2√3
x-x√3=2-2√3
x(1-√3)=2-2√3 /*(1+√3)
x(1-√3)(1+√3)=(2-2√3)(1+√3)
x(1²-(√3)²)=2+2√3-2√3-2√3*√3
x(1-3)=2-6
-2x=-4 /:(-2)
x=2
d) (3-√3)(x+√3)=4-√3
3x+3√3-√3x-√3*√3=4-√3
(3-√3)x=4-√3-3√3+3
(3-√3)x=7-4√3 /*(3+√3)
(3-√3)(3+√3)x=(7-4√3)(3+√3)
(3²-(√3)²)x=21+7√3-12√3-12
(9-3)x=9-5√3
6x=9-5√3 /:6
x=(9/6)-(5/6)√3
x=(3/2)-(5/6)√3
e) (5-√5)(x+√5)=4-√5
5x-√5x+5√5-√5*√5=4-√5
(5-√5)x=4-√5-5√5+5
(5-√5)x=9-6√5 /*(5+√5)
(5-√5)(5+√5)x=(9-6√5)(5+√5)
(5²-(√5)²)x=45+9√5-30√5-6√5*√5
(25-5)x=-21√5+15
20x=-21√5+15 /:20
x=-(21/20)√5+(15/20)
x=-(21/20)√5+(3/4)
f) (3x(√3+2)=√3(4x-5)
3√3x+6x=4√3x-5√3
3√3x+6x-4√3x=-5√3
6x-√3x=-5√3
(6-√3)x=5√3 /*(6+√3)
(6-√3)(6+√3)x=5√3(6+√3)
(6²-(√3)²)x=30√3+15
(36-3)x=30√3+15
33x=30√3+15 /:33
x=(30/33)√3+(15/33)
x=(10/11)√3+(5/11)
g) 2¹⁷*x-16⁴*3=5(4⁸*x-32¹⁷)
2¹⁷x-(2⁴)⁴*3=5*(2²)⁸x-5*(2⁵)¹⁷
2¹⁷x-3*2¹⁶=5*2¹⁶x-5*2⁸⁵ /:2¹⁶
x-3=5x-5*2⁶⁹
x-5x=3-5*2⁶⁹
-4x=3-5*2⁶⁹ /:(-4)
x=(-3/4)+5*2⁶⁹*2⁻²
x=(-3/4)+5*2⁶⁷
h) 27³* 2x-3⁹=3¹⁰*x+2*3⁹
(3³)³*2x-3⁹=3¹⁰x+2*3⁹
3⁹*2x-3⁹=3¹⁰x+2*3⁹ /:3⁹
2x-1=3x+2
2x-3x=2+1
-x=3 /:(-1)
x=-3
i) 3¹³*x-4*9⁶=27⁴(2x-5)
3¹³x-4*(3²)⁶=(3³)⁴(2x-5)
3¹³x-4*3¹²=3¹²(2x-5) /:3¹²
3x-4=2x-5
3x-2x=-5+4
x=-1
j) (4⁵*x+32²)*2⁵=2¹⁶*x
((2²)⁵x+(2⁵)²)*2⁵=2¹⁶x
(2¹⁰x+2¹⁰)*2⁵=2¹⁶x
2¹⁵x+2¹⁵=2¹⁶x /:2¹⁵
x+1=2x
x-2x=-1
-x=-1 /:(-1)
x=1
7x-4√3x+7√3-4√3*√3=6
x(7-4√3)+7√3-12=6
x(7-4√3)=6+12-7√3
x(7-4√3)=18-7√3 /*(7+4√3)
x(7-4√3)(7+4√3)=(18-7√3)(7+4√3)
x(7²-(4√3)²)=126+72√3-49√3-84
x(49-48)=42+23√3
x*1=42+23√3
x=42+23√3
b) x√7+3=x-5
x√7-x=-5-3
x(√7-1)=-8 /*(√7+1)
x(√7-1)(√7+1)=-8(√7+1)
x((√7)²-1²)=-8√7-8
x(7-1)=-8√7-8
6x=-8√7-8 /:6
x=(-8/6)√7-8/6
x=(-4/3)√7-4/3
c) x-2=x√3-2√3
x-x√3=2-2√3
x(1-√3)=2-2√3 /*(1+√3)
x(1-√3)(1+√3)=(2-2√3)(1+√3)
x(1²-(√3)²)=2+2√3-2√3-2√3*√3
x(1-3)=2-6
-2x=-4 /:(-2)
x=2
d) (3-√3)(x+√3)=4-√3
3x+3√3-√3x-√3*√3=4-√3
(3-√3)x=4-√3-3√3+3
(3-√3)x=7-4√3 /*(3+√3)
(3-√3)(3+√3)x=(7-4√3)(3+√3)
(3²-(√3)²)x=21+7√3-12√3-12
(9-3)x=9-5√3
6x=9-5√3 /:6
x=(9/6)-(5/6)√3
x=(3/2)-(5/6)√3
e) (5-√5)(x+√5)=4-√5
5x-√5x+5√5-√5*√5=4-√5
(5-√5)x=4-√5-5√5+5
(5-√5)x=9-6√5 /*(5+√5)
(5-√5)(5+√5)x=(9-6√5)(5+√5)
(5²-(√5)²)x=45+9√5-30√5-6√5*√5
(25-5)x=-21√5+15
20x=-21√5+15 /:20
x=-(21/20)√5+(15/20)
x=-(21/20)√5+(3/4)
f) (3x(√3+2)=√3(4x-5)
3√3x+6x=4√3x-5√3
3√3x+6x-4√3x=-5√3
6x-√3x=-5√3
(6-√3)x=5√3 /*(6+√3)
(6-√3)(6+√3)x=5√3(6+√3)
(6²-(√3)²)x=30√3+15
(36-3)x=30√3+15
33x=30√3+15 /:33
x=(30/33)√3+(15/33)
x=(10/11)√3+(5/11)
g) 2¹⁷*x-16⁴*3=5(4⁸*x-32¹⁷)
2¹⁷x-(2⁴)⁴*3=5*(2²)⁸x-5*(2⁵)¹⁷
2¹⁷x-3*2¹⁶=5*2¹⁶x-5*2⁸⁵ /:2¹⁶
x-3=5x-5*2⁶⁹
x-5x=3-5*2⁶⁹
-4x=3-5*2⁶⁹ /:(-4)
x=(-3/4)+5*2⁶⁹*2⁻²
x=(-3/4)+5*2⁶⁷
h) 27³* 2x-3⁹=3¹⁰*x+2*3⁹
(3³)³*2x-3⁹=3¹⁰x+2*3⁹
3⁹*2x-3⁹=3¹⁰x+2*3⁹ /:3⁹
2x-1=3x+2
2x-3x=2+1
-x=3 /:(-1)
x=-3
i) 3¹³*x-4*9⁶=27⁴(2x-5)
3¹³x-4*(3²)⁶=(3³)⁴(2x-5)
3¹³x-4*3¹²=3¹²(2x-5) /:3¹²
3x-4=2x-5
3x-2x=-5+4
x=-1
j) (4⁵*x+32²)*2⁵=2¹⁶*x
((2²)⁵x+(2⁵)²)*2⁵=2¹⁶x
(2¹⁰x+2¹⁰)*2⁵=2¹⁶x
2¹⁵x+2¹⁵=2¹⁶x /:2¹⁵
x+1=2x
x-2x=-1
-x=-1 /:(-1)
x=1