załącznik
1.
3√64-√8+√16+√32 = 3·8-√(4·2)+4+√(16·2) = 24-√4·√2+4+√16·√2 = 28-2√2+4√2 = 28+2√2
2.
x = 2-3√5, y = 2+3√5
x+y = 2-3√5+2+3√5 = 4
x-y = 2-3√5-(2+3√5) = 2-3√5-2-3√5 = -6√5
x·y = (2-3√5)(2+3√5) = 2²-(3√5)² = 4-9·5 = 4-45 = -41
x/y = (2-3√5)/(2+3√5) · (2-3√5)/(2-3√5) = (2-3√5)²/((2²-(3√5)²) = (4-12√5+45)/(4-45) =
= (49-12√5)/(-41) = (12√5-49)/41
1)
3√64-√8+√16+√32 =
= 3 * 8 - √(4*2) + 4 + √(16*2) =
= 24 - 2√2 + 4 + 4√2 =
= 28 + 2√2=
= 2(14+2√2)
2)
x+y :
2-3√5+2+3√5 =
=2 + 2 - 3√5 + 3√5 =
=4-0 = 4
x-y :
2-3√5-2-3√5 =
=2-2 - 3√5 - 3√5=
=-6√5
x * y :
(2-3√5)(2+3√5) =
=4 - (3√5)² =
=4 - 45 =
=-41
x: y :
2-3√5/2+3√5 * (2-3√5)/(2-3√5) =
=(2-3√5)²/(4 - (3√5)²) =
=(4 - 12√5 + 45)/ (4 - 45)=
=(49 - 12√5) /(-41)=
=-(-49 +12√5) /(-41) =
= (-49 + 12 √5) / 41
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1.
3√64-√8+√16+√32 = 3·8-√(4·2)+4+√(16·2) = 24-√4·√2+4+√16·√2 = 28-2√2+4√2 = 28+2√2
2.
x = 2-3√5, y = 2+3√5
x+y = 2-3√5+2+3√5 = 4
x-y = 2-3√5-(2+3√5) = 2-3√5-2-3√5 = -6√5
x·y = (2-3√5)(2+3√5) = 2²-(3√5)² = 4-9·5 = 4-45 = -41
x/y = (2-3√5)/(2+3√5) · (2-3√5)/(2-3√5) = (2-3√5)²/((2²-(3√5)²) = (4-12√5+45)/(4-45) =
= (49-12√5)/(-41) = (12√5-49)/41
1)
3√64-√8+√16+√32 =
= 3 * 8 - √(4*2) + 4 + √(16*2) =
= 24 - 2√2 + 4 + 4√2 =
= 28 + 2√2=
= 2(14+2√2)
2)
x+y :
2-3√5+2+3√5 =
=2 + 2 - 3√5 + 3√5 =
=4-0 = 4
x-y :
2-3√5-2-3√5 =
=2-2 - 3√5 - 3√5=
=-6√5
x * y :
(2-3√5)(2+3√5) =
=4 - (3√5)² =
=4 - 45 =
=-41
x: y :
2-3√5/2+3√5 * (2-3√5)/(2-3√5) =
=(2-3√5)²/(4 - (3√5)²) =
=(4 - 12√5 + 45)/ (4 - 45)=
=(49 - 12√5) /(-41)=
=-(-49 +12√5) /(-41) =
= (-49 + 12 √5) / 41