Questions (1 Viewer)

[KimmorleyKiller]

Rationalise the denominator and simplify

1/5+root2  +  4/2-root3

Solve

x^2-6x-7<0

Factorise:

2p^3+128

2x^2y-8y^3

8x^3-27y^3

Solve

1/x-1 less than\equal to 3

rationalise denom and simplify

3+root5+1/3+root5

Simplify

2a^2b+10ab/b^3+27 divided by a^2-25/4b+12

Cheers, KK!

 

[SoulSearcher]

Hmm ok then, but these seem easy

Rationalise the denominator and simplify

1/5+root2 + 4/2-root3

1 / (5+sqrt2) + 4 / (2-sqrt3)
= (5-sqrt2) / 21 + 4(2-sqrt3)
= (5 - sqrt2 + 168 + 81sqrt3) / 23
= (173 - sqrt2 + 81sqrt3) / 23

Solve

x^2-6x-7<0

x² - 6x - 7 < 0
(x-7)(1+1) < 0
test x = 0
-7 * 1 = -7, smaller than 0, therefore -1 < x < 7

Factorise:

2p^3+128

2x^2y-8y^3

8x^3-27y^3

2(p+4)(p² -4p + 16)
2(x^2y - 4³)
(2x-3y)(4x² + 6xy + 9y²)

Solve

1/x-1 less than\equal to 3

1/(x-1) < 3
(x-1) < 3(x-1)²
3x² - 7x + 4 > 0
(3x-4)(x-1)>0
test x = 1.1
-0.7 * 0.1 = -0.07, not larger than 0, therefore x > 4/3 or x < 1

rationalise denom and simplify

3+root5+1/3+root5

(3+root5 / 3+root5) + 1 / 3+root5
= 1 + 1 / 3+root5
= 1 + (3-root5) / 4
= (7 - root5) / 4

Simplify

2a^2b+10ab/b^3+27 divided by a^2-25/4b+12

Can't be bothered doing that one

 

[Trev]

[2a²b+10ab]/[b³+27] * [4b+12]/[a²-25]
[2ab(a+5)]/[(b+3)(b²-3b+9)] * [4(b+3)]/[(a+5)(a-5)]
[8ab]/[(a-5)(b²-3b+9)]
I don't see it going any further...

 

[Loz_metalhead]

Hmm ok then, but these seem easy


1 / (5+sqrt2) + 4 / (2-sqrt3)
= (5-sqrt2) / 21 + 4(2-sqrt3)
= (5 - sqrt2 + 168 + 81sqrt3) / 21
= (173 - sqrt2 + 81sqrt3) / 21

shouldn't it be over 23...

I got (189 - sqrt2 + 92sqrt3) / 23

...cant see where I went wrong...lol.
:wave:

 

[Trev]

Yeah, it's over 23 not 21.

 

[SoulSearcher]

Whoops, all fixed now.