#I have no idea what this is asking for? Anyone know where I can learn this topic?

73 messages · Page 1 of 1 (latest)

arctic cedar
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Those are just "hidden quadratics"

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make a substitution

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so using a as an example

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we have x⁶ + 9x³ + 8

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that's the same as

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(x³)² + 9x³ + 8

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so let's make a substitution

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let u = x³

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we get u² + 9u + 8 = 0

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which looks more approachable now

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u is just a random variable

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well $(a^m)^n = a^{m × n}$

regal shellBOT
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AmbivalentChamp

478976978880299012.png
opaque igloo
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i thought this was gcse for a second

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now i want to learn this

arctic cedar
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To show you that it looks like a quadratic

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You notice how the leading power is always double the second terms power

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Like x⁶ and x³

opaque igloo
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then replace u with x^3

arctic cedar
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It's the same way as x² and x

opaque igloo
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so (x^3+8)(x^3+1)

arctic cedar
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u is x³

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We just set u = x³ to make it simpler

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make our own substitution

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so the question becomes more easier to interpret

rugged fossil
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my teacher calls it a hidden quadratic. u can try searching that

arctic cedar
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Well now you have x³ + 8 = 0 and x³ + 1 = 0

opaque igloo
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for q c

rugged fossil
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I feel like it's hard to explain without showing ur working out. this is quite messy!

arctic cedar
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and then solve that for x

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Yeah

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Well x³ = -8 and x³ = -1

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cube root

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yeah

rugged fossil
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which questions r u doing?

arctic cedar
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I have the brain of a y10 so

opaque igloo
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is it (3x^3)^3 for c

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or what

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as replacement for 27x^6

arctic cedar
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yeah

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But the point is just make a substitution to simplify it for yourself

opaque igloo
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so then how would u factorise a cubic

arctic cedar
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which question sorry?

opaque igloo
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hidden cubic now?

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c

arctic cedar
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27x⁶ + 26x³ - 1 = 0

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= 27(x³)² + 26x³ - 1 = 0

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so let u = x³ again

opaque igloo
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oh that simple

arctic cedar
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27u² + 26u - 1 = 0

arctic cedar
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Without having to make a sub

opaque igloo
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so for d
$32x^{10}-33x^{5}+1$

regal shellBOT
opaque igloo
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is

rugged fossil
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this is how i do it btw!

image0.jpg
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@flat path

arctic cedar
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Samsung tablet

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Good man

opaque igloo
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$32(x^{5})^{2}-33x^{5}+1$

regal shellBOT
rugged fossil
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aha i don't have a Samsung tablet

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I use my phone

opaque igloo
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and let u = x^5

arctic cedar
rugged fossil
opaque igloo
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what are them gcse qs that require u to replace an expression with a single letter

arctic cedar
opaque igloo
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cos this is kinda similar to that

rugged fossil
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I don't use the Samsung tablet to do my work cuz it's a family one and it's not very clean lollerz